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Detailed Solutions
Advanced Exam Pack
Volume 2
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1"
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This publication assists applicants for Year 9 entry to selective high schools to become more
familiar with the Selective Schools Entrance Examination.
The Selective Schools Entrance Examination measures ability and is set to discriminate at a
very high level. Students who are accustomed to answering most questions in tests correctly
should not be discouraged if they get a number of questions wrong. It is very rare for even the
highest scoring candidates to score full marks on all components of the Selective Schools
Entrance Examination.
Please note that the information contained on in these pages and any study materials
published by Spectrum Tuition Pty Ltd is for informational purposes only, which is to be used
as a study tool for the Selective Schools’ Entrance Examination.
Spectrum Tuition Pty Ltd has made reasonable efforts to provide current and accurate
information to readers. The author will not be held liable for any unintentional errors or
omissions that may be found. Spectrum Tuition is not affiliated, approved or endorsed by
Edutest™ or the Australian Council of Educational Research.
No part of this document shall be reproduced or transmitted, in whole or in part in any form,
without the prior written consent of the author.
It is important to note that summaries, methods of study, tips and tricks are only
recommendations from the author. Reading any information on www.spectrumtuition.com
and any study materials published by the author does not itself guarantee high scores on the
Selective Schools Entrance Exam. You have to do your part of preparing by studying for the
exam adequately.
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CONTENTS PAGE
Test Pack 1
1. Numerical reasoning
4
2. Verbal reasoning
25
3. Mathematical reasoning
38
4. Reading comprehension
61
Test Pack 2
1. Numerical reasoning
68
2. Verbal reasoning
80
3. Mathematical reasoning
94
4. Reading comprehension
113
Test Pack 3
1. Numerical reasoning
122
2. Verbal reasoning
133
3. Mathematical reasoning
151
4. Reading comprehension
180
©"SPECTRUM TUITION PTY LTD
3"
NUMERICAL REASONING
EXAM PAPER 1
Detailed Solutions
Question 1: D – 6, 12
Steps
1. Define the variables
2. Formulate the equation
3. Expand the bracket
4. Combine the like terms
5. Deduct 12 from both sides of the
equation
6. Divide both sides of the equation
by 3 to find a (the smaller number)
7. Find the larger number
8. Find the answer
Working
Let “a” be the smaller number.
The larger number is 6 more than the smaller
number = a + 6
The question states that the smaller and two
times the larger is 30
a + 2(a + 6) = 30
a + 2a + 12 = 30
3a + 12 = 30
3a + 12 = 30
3a + 12 - 12 = 30 - 12
3a = 18
a = 6-the smaller number.
Therefore, the larger number is
a + 6 = 6 + 6 = 12.
The two numbers are therefore 6 and 12
Question 2: E – None of these
Steps
1. Determine the difference between
each number going horizontally and
vertically.
2. Find the missing number
©"SPECTRUM TUITION PTY LTD
Working
In this case, the difference between numbers
horizontally is 3 and vertically it is 4
16 – 13 = 3
13 – 10 = 3
10 – 7 = 3
16 – 12 = 4
12 – 8 = 4
16 13 10 7
12
9
6 3
8
5
2 ?
Subtract 4 from 3 = 3 – 4 = -1
4"
Question 3: B – 24
Steps
1. Define the variables
2. Set up a pair of simultaneous
equations
Working
Let: x = the number of 12 kg containers.
y = the number of 9 kg containers.
Given the company truck carries 50
containers weighing a total of 528 kilograms.
x + y = 50…..Eq.1
12x + 9y = 528…..Eq.2
3. Multiply Eq. 1 by 12:
12x + 12y = 600…Eq.3
4. Subtract Eq.2 from Eq.3 to
eliminate x
12x + 9y = 528…..Eq.2
-(12x + 12y = 600)…Eq.3
5. Divide both sides by -3 to find the
value of y
- 3y = -72
-3
-3
y = 24
The number of 9 kilogram containers = 24
6. Answer the question
Question 4: D – 26
Steps
1. Given that we have the value for y,
substitute into equation 1 to find the
value of x
2. Subtract 24 from each side or move
24 to the other side of the equals sign
then change the sign
3. Find the value for x
Working
x + 24 = 50
4. Answer the question
The number of 12 kilogram containers = 26
x + 24 – 24 = 50 – 24
x = 26
Question 5: B – 3
Steps
1. Find out the least number of socks
the person can pull out in the dark to
be sure he has a matching pair.
Working
There are only two colours (brown and blue),
so pulling out three socks will guarantee that
two will be of the same colour.
Question 6: D – 40
Steps
1. Find out the pattern followed by
the numbers in the circles.
2. Find out the missing number.
©"SPECTRUM TUITION PTY LTD
Working
The numbers in the circles go together this
way: first number divided by 3 gives you the
second number.
Therefore in the third circle 120 ÷ 3 = 40
5"
Question 7: A - 6:20 pm
Step 1: Create a table to show the time on the clock in relation to the real time as each
hour passes. For each hour, 15 minutes are lost.
Real time
Clock
1.00pm
2.00pm
1.45pm
3.00pm
2:30pm
4.00pm
3.15pm
5.00pm
4.00pm
6:00pm
4:45pm
7:00pm
5:30pm
Step 2: We need to determine what the actual time is when the clock reads 5:00pm.
According to the table, when the clock reads 4.45pm, it is 6:00pm so we have to
determine what each minute on the clock is equivalent to in real time.
Step 3: Each minute on the clock can be calculated as 60/45 = 1.33
Step 4: Multiply this by the 15 minutes remaining from 4:45pm – 5:00pm
1.33 x 15 = 20 minutes
Step 5: Answer the question. The time is therefore 6.20pm when the clock reads
5:00pm.
Question 8: C - 5 ¼ kg
Steps
1. Write the equation to find out
Kwame’s total weight loss as at the
end of week four.
2. Convert the mixed numbers to
improper fractions
3. Find the lowest common
denominator. In this case, it’s 8
4. Add the fractions
5. Convert the improper fraction to a
mixed number and simplify.
©"SPECTRUM TUITION PTY LTD
Working
!
!
Given Kwame lost 1! kg in the first week,!!
!
kg in the second week, 2! kg in week three
!
and ! kg in week four
Kwame’s total weight loss as at the end of
1 7
1 3
week four = 1 + + 2 +
8 8
2 4
9 7 5 3
= + + +
8 8 2 4
9 7 5 ×4 3×2
+ +
+
8 8 2 ×4 4 ×2
9 7 20 6
+
= + +
8 8 8 8
42
=
8
2
1
=5 =5
8
4
6"
Question 9: B- 6
Steps
1. Define the variables
Working
Let b represent Bella’s age.
Let s represent Stella’s age.
2. Determine the relationship between If Bella will be 10 years older than Stella in 5
Bella and Stella’s age from given
years, then she is also 10 years older than her
statements.
now. Therefore,
b = s + 10
In 5 years, the sum of Bella and Stella’s ages
will be 32. Therefore,
b + 5 + s + 5 = 32
b + s + 10 = 32
3. Substitute b = s + 10 into the
second equation
4. Solve for s
7. Answer the question.
b = s + 10
b + s + 10 = 32
Therefore,
s + 10 + s + 10 = 32
s + 10 + s + 10 = 32
2s + 20 = 32
2s = 12
s=6
Stella is 6 years now.
Note: you could also use trial and error to
check each possible answer.
Question 10: D- 81
Steps
1. Find out the pattern followed
by the numbers in the9series.
2. Find out the missing number.
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Working
The given series:
9, 27 ,?, 243 ,729 ,2187
The series follows the following pattern:
9× 3 = 27
81 × 3 = 243
243 × 3 = 729
729 × 3 = 2187
From the foregoing
27 × 3 = 81
7"
Question 11: B – 102
Steps
1. Find out the
pattern followed by
the numbers in the
series.
2. Find out the
missing number.
Working
The given series: ? ,105, 99, 102, 96, 99, 93
The series alternates the following operations + 3, −6
Therefore
Therefore:
105 – 6 = 99
99 + 3 = 102
102 – 6 = 96
96 + 3 = 99
From the foregoing the missing number represented by the ?
can be found by reversing the first operation by subtracting
3 from 105. 105 – 3 = 102
Question 12: A – 75
Steps
Working
1. Determine the pattern
followed by numbers in the grid.
2. Answer the question
?
63
69
57
54
42
58
52
37
As we move from top to bottom 12 is subtracted at
first step and 5 is subtracted at next step.
Adding 12 to 63 gives us the number 75.
Question 13: C – 32km
Steps
1. Define the variables
2. Determine the formula to calculate
distance
2. Formulate the equation
3. Expand the bracket
4. Combine the like terms
5. Divide both sides of the equation
by 12
7. Find the total distance Martin runs
every morning.
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Working
Let a = distance uphill
b = distance downhill
c = distance on level grounds
t = 8 hours
Distance (d) = Speed (s) × Time (t)
!∴t = d / s
!
!
!
!
!
!
8=( !+!+ !)+( !+!+ !)
!!!!!!!!
!!!!!!!!
8=
+
!"
!"
8 × 24 = 8a + 4b + 6c + 4a + 8b + 6c
192 = 8a + 4b + 6c + 4a + 8b + 6c
192 = 12a + 12b + 12c
192 = 12(a + b + c)
16 = (a + b + c)
Martin covers the same distance twice i.e.
going and returning: 16km × 2 = 32 km
Martin jogs over a distance of 32 km every
morning.
8"
Question 14: C - $4.60
Steps
1. Define the variables.
2. Given Kofi wanted to
purchase 2 dozen eggs and a
bottle of milk. Those items
cost $9.40.
3. Also given the money he had
on him at that moment was
not adequate, so he decided to
purchase 6 fewer eggs and
paid $8.20.
4. Solve the equations 1 and 2
by subtracting Eq.2 from
Eq.1
Working
Let e = the price of an egg.
m = the price of a bottle of milk
24e + m = 9.40…..Eq.1
(24 − 6) e + m = 8.20
18e + m = 8.20…..Eq.2
(24e + m) – (18e + m) = 9.40 – 8.20
6e = 1.20
e = 0.20
5. Determine the price of a bottle Substitute e into Eq.1:
of milk.
24(0.20) + m = 9.40
4.80 + m = 9.40
m = 9.40 – 4.80
m = 4.60
The price of a bottle of milk = $4.60
Question 15: C - 105
Steps
1. Convert all units to metres
2. Determine the volume of both
carton and container. Volume
is determined by the
following formula:
Length x Width x Height
3. Determine the number of
cartons that can be packed
into the container.
4. To divide decimals, multiply
the divisor, as well as the
dividend by 10
Working
80cm = 0.80
Volume of cartons:
2!× 2 × 0.8 = 3.2 cubic metres.
Volume of container:
8!× 7 ×!6 = 336 cubic metres
Number of cartons that can fit into the
container
= Volume of container/ Volume of cartons
= 336/3.2
3.2 336 =" 32 3360 "
5. Complete the division
105
32 33160 "
6. Complete the sum
The number of cartons that can be packed
into a container is therefore 105.
©"SPECTRUM TUITION PTY LTD
9"
Question 16: D – 100%
Steps
1. Define the variable
Working
Let x = the mark on the 7th exam.
2. Given Bob got an average of
65% on his first 6 exam
papers.
3. Find the marks Bob would
have to obtain on the 7th and
final exam paper so he gets an
average of 70% on all
7 exams papers.
(Sum of marks on 6 papers)/6 = 0.65
Sum of marks on 6 papers = 0.65 × 6
= 3.90
The average of 7 papers such that the average
equals 70%:
(0.65 × 6 + x)/7 = 0.70
4. Multiply each side by 7
5. Subtract each side by 3.90
6. Solve for x.
3.90 + x = 0.70 × 7
3.90 + x = 4.90
3.90 + x = 4.90
x = 4.90 − 3.90
x = 1 (100% i.e. 1×100 )
The marks Bob would have to obtain on the
7th and final exam paper so he gets an
average of 70% on all 7 exams papers is
100%.
Question 17: A – 100
Steps
1. Find out the pattern followed
by the numbers in the circles.
Working
Operations in circle 2:
220– 20 = 200 (first number in the second
circle)
15 – 2 = 13(second number in second circle)
Operations in circle 3:
200 – 40 = 160 (first number in the third
circle)
13 – 4 = 9(second number in the third circle)
2. Find out the missing
number.
Following from the pattern above:
Operations in circle 4:
160 – 60 = 100 (first number in the fourth
circle. The pattern is that the first number is
reduced by a multiple of 20 from one circle
to the next going from left to right)
9 - 6 = 3 (second number in the fourth circle.
The pattern is that the second number reduces
by a multiple of 2 from one circle to the next
going from left to right)
©"SPECTRUM TUITION PTY LTD
10"
Question 18: A – 19
Steps
1. Determine the pattern
followed by numbers in the
grid.
2. Answer the question
Working
67
55
63
51
55
43
51
39
42
30
38
26
35
23
31
?
As we move from top to bottom the pattern
followed is: -8, +8, -12
Subtracting 12 from 31 :
31 – 12 = 19
Question 19: B – 15%
Steps
1. Define the variable.
2. Given a green grocery
store in Adelaide bought
640 oranges from a
university farm for $192.
Some of these oranges
were spoilt and so they
were thrown away
3. Determine the formula
for the selling price.
Working
Let x = the number of oranges thrown
Number of oranges left = 640 – x
Selling Price (SP) –!Cost Price (CP) = Profit (P)
∴ Selling Price (SP) = Cost Price (CP) + Profit (P)
4. Given the store sold the
remainder oranges at 40
cents each thus making a
profit of $25.60.
5. Solve for x.
Substitute the Cost price and profit in the above
equation to find Selling Price
0.40(640!− x) = 192 + 25.60
6. Find out the percentage
of the oranges that was
thrown away.
Percentage = 96/640 × 100 = 15%
©"SPECTRUM TUITION PTY LTD
256 – 0.40 x = 192 + 25.60
256 – 0.40x = 217.60
256 – 217.60 = 0.40x
38.40/0.40 = x
x = 96
11"
Question 20: C – $22 million
Steps
1. Find the number of seconds in
a day.
2. Determine the amount Bill
Gates will make in a day
Working
We know 60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
Number of seconds in a day =
60 × 60 × 24 = 86,400 seconds (1 day)
Given Bill Gates, earns US$250 every second
The amount Bill Gates will make in a day =
86,400 × 250 = 21,600,000
(to the nearest million = 22 million)
Question 21: C – $8 billion
Steps
1. Find number of seconds in a
day.
2. Determine the amount Bill
Gates will make in a day
3. Determine the amount Bill
Gates will make in a year.
Working
We know 60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
Number of seconds in a day =
60 × 60 × 24 = 86,400 seconds (1 day)
Given Bill Gates, earns US$250 every second
The amount Bill Gates will make in a day =
86,400 × 250 = 21,600,000
Number of days in a year = 365
The amount Bill Gates will make in a year
= $21,600,000 × 365
= $7,884,000,000
(Roundup to the nearest billion)
Answer rounded up to the nearest billion:
$8,000,000,000/ $8 billion
Question 22: D – $360
Steps
1. Find out the amount Andreas
will have to spend to fuel up
the new car for a year
Working
Given Ali pays $600 per year to fuel up the
car Andreas currently drives costs 1/5 less to
fuel up than Ali’s car.
The sales woman claims that, Andreas will
pay 1/4 less for petrol than he currently pays
for his old car.
The amount Andreas will have to spend to
fuel up the new car for a year =
$600.00 × (4/5) × (3/4) = $360.00
©"SPECTRUM TUITION PTY LTD
12"
Question 23: D – M
To find the number or letter that should be in the square marked by the question mark
you must carefully inspect the pattern formed by the existing numbers and letters and
make some assumptions.
In the grid you can assume that if all the numbers and letters were in place they would
form an L-shaped pattern i.e.╚. It appears the letters are consecutive .i.e. in the
normal order of letters in the English language and the numbers are also consecutive.
Following from assumptions and observations you could start with the first columnsixth row. The consecutive letters I-S in the first column-sixth row together will form
an L-shaped pattern. For the second column-fifth row we have the numbers 1-9
forming the L-shaped pattern. It follows from there that the L-shape formed out of the
third column-fourth row would have consecutive letters I-O filling seven squares to
form the L-shaped pattern, therefore the square marked by the question mark would
have the letter “M”. The correct answer is D.
Question 24: C – $125
Steps
Working
1. Work out the quantity of the third item, 10 wedding hats cost $500 each and so it
wedding gowns
would amount to $5,000 in all.
The boutique owner bought 20 dark
sunglasses. With the knowledge of these
two quantities i.e.10 + 20 = 30, we are
able to work out the quantity of the third
item, wedding gowns i.e. 45 – 30 = 15 .
2. Calculate the total cost of wedding
gowns
3. With knowledge of the total cost of
wedding hats ($5,000) and wedding
gowns ($22,500) we can compute the
total cost for the 20 dark sunglasses
©"SPECTRUM TUITION PTY LTD
15 × $1,500 = $22,500.
$30,000 - $5,000- $22,500 = $2,500.
$2,500 ÷ 20 = $125 –price for each pair
of dark sunglasses.
13"
Question 25: C – 29
Steps
1. Define the variables.
Working
Let p = total number of pebbles
b = total number of black pebbles
g = total number of green pebbles
y = total number of yellow pebbles
2. Given that there are a total of b + g + y = p = 112………..Eq.1
112 pebbles in the jar.
3. Given that there are twice as b = 2 × g…………………..Eq.2
many black pebbles as green
pebbles.
4. Given that there are 4 less y = g – 4……………………Eq.3
yellow pebbles than green
pebbles.
5. Substitute b and g into Eq.1
b + g + y = 112
(2 × g) + g + (g – 4) = 112
6. Determine the number of
Substitute b and g into Eq.1
green pebbles in the jar by
b + g + y = 112
solving for g.
(2 × g) + g + (g – 4) = 112
2g + 2g – 4 = 112
4g – 4 = 112
4g = 112 + 4
4g = 116
g = 29
Question 26: A –25
1. Find out the number of
yellow pebbles in the jar.
©"SPECTRUM TUITION PTY LTD
Substitute g into Eq.3
y=g–4
y = 29 – 4
y = 25
14"
Question 27: A –1190 km
Steps
1. . Define the variables
2. Determine the formula to
calculate distance.
3. Find out the distance
travelled on the four-wheel
drive.
Working
Let t = the time spent on bus and 4-wheel
drive.
Distance (d) = Speed × Time (t)
Given the four-wheel drive travelled at an
average speed of 60 km per hour
The distance travelled on the four-wheel drive
= 60t
4. Find out the distance travelled Given Michael travelled 170 km more on the
on the bus.
bus.
5. Find out the value of t.
6. Find out the total distance
travelled on the bus and fourwheel drive.
©"SPECTRUM TUITION PTY LTD
Distance travelled on the bus = 60t + 170
t=d/s
Given the bus travelled at an average speed of
80 km per hour.
t = (60t + 170)/ 80
80t = 60t + 170
80t – 60t = 170
20t = 170
t = 170/20
t = 8.5
Total distance = distance spent on four-wheel
drive + distance spent on bus
= 60t + (60t + 170)
= 60(8.5) + 60(8.5) + 170
= 510 + 510 + 170
= 1190 km
15"
Question 28: D - $70,600
Salary Scale & Rebates
80,000 - Below:
Working parents in this category receive a rebate on health care expenses for kids of
65% plus a medical expenses bonus of $2,000 (this only applies to this category of
earnings).
80,001 - 100,000
Working parents in this category receive a rebate on health care expenses for kids of
45%
100,001 - Above
Working parents in this category receive a rebate on health care expenses for kids of
25%
1. Janet & James earn $100,001, so they get a 25% rebate. Making their afterrebate cost on health care for kids: 75% (i.e.100%-25%) x $30,000 =
$22,500. So their net would be $100,001 - $22,500 = $77,501.
2. Esther & Emmanuel earn $96,000, so they get a 45% rebate. Making their
after-rebate cost on health care for kids: 55% x $30,000 = $16,500. So their
net would be $96,000 - $16,500 = $79,500.
3. Lucy & Leslie earn $79,100, so they get a 65% rebate plus a bonus of $2,000.
Making their after-rebate cost on health care for kids: 35% x $30,000 =
$10,500. So their net including the bonus is $79,100 - $10,500 + $2,000 =
$70,600.
Question 29: C - 1331
Steps
1. Find out the pattern followed
by the numbers in the series.
Working
The given series:
8,64,512 9,81,729
6,36,216 11, 121,?
Through trial and error we can see that the
numbers in the other three boxes follow this
pattern: x, x ! , x !
2. Find out the missing number.
©"SPECTRUM TUITION PTY LTD
Therefore to get the missing number 11! =
1331
16"
Question 30: C – 25
Steps
1. Determine the equation
Working
Let x represent the fifth number.
Given the average of these five numbers is 30
(x + 18 + 27 + 32 + 48)
= 30
5
x = 150 – 125
x = 25
2. Add the numbers in the
brackets together
3. Multiply each side by 5
4. Subtract 125 from both sides
(x + 125)
= 30
5
x + 125 = 30 × 5
"
x + 125 = 150
x = 150 − 125
"
x = 25
Question 31: A – Ford E-350
Steps
1. Multiply the number of larger
boxes for each van by 12
(smaller boxes that can go into
each larger box) and attempt to
subtract 24 from each result
2. Answer the question
Working
Ford E-350:
4× 12 = 48 – 24 = 24
Chevrolet Astro: 16 × 12 = 192 – 24 = 168
Chevrolet Express: 14 ×12 = 168 – 24 = 144
Ford Transit:
8 × 12 = 96 – 24 = 72
GMC Safari:
6 × 12 = 72 – 24 = 48
Dodge Caravan: 12 × 12 = 144–24 = 120
The Ford E-350 can carry 24 smaller boxes with
the least amount of room left over:
Question 32: A - 1
To transport 144 smaller boxes, you need to have space for 12 larger boxes.
Since you're not supposed to have space left, can you find a van or combination of
vans that together carry exactly 12 larger boxes?
Option 1: The Dodge Caravan can carry exactly 12 larger boxes.
Option2: The Ford E-350 and the Ford Transit can together carry exactly 12 larger
boxes.
The obvious answer would be option 1-a single van
©"SPECTRUM TUITION PTY LTD
17"
Question 33: B - $36
You need 60/12= 5 larger boxes.
The GMC Safari can carry 6 larger boxes at $36 (Remember left over spaces are
allowed)
Question 34: C – 15, 40
Steps
1. Define the variables
2. Construct the equation
3. “The bigger number equals 3 times the
smaller number, reduced by 5”
4. Substitute value of x
Working
Let x = smaller number
y = bigger number
Given the sum of two numbers is 55.
x + y = 55
x + (3x – 5) = 55
x + 3x – 5 = 55
4x = 60
x = 15
15 + y = 55
y = 55 −15
y = 40
Question 35: B – 75
Steps
1. Define the variables
Working
Let a = the number of questions they
answered correctly.
b = the number of questions they did not
make any attempts to answer
c = the number of questions they answered
incorrectly.
2. Find out the relationship
0 ≤ a, b, c ≤ 120
between the number of
a + b + c = 120 (number of questions)… Eq 1
questions answered correctly,
3a – c = 180 (score)………………….Eq 2
incorrectly and unanswered.
Adding the two equations:
4a + b = 300
3. Find out the maximum Let b = 0; we are assuming they attempted to
number of questions the answer all 120 questions.
representatives from Eastside
High could have answered You want “ a” to be as high as possible, while
correctly.
keeping “b” non-negative, so just divide 300
by 4 i.e.
4a + 0 = 300
a = 300/4 = 75
©"SPECTRUM TUITION PTY LTD
18"
Question 36: E – None of these
Steps
1. Find out the pattern
followed by the
numbers in the
series.
Working
The given series:
36, 63,108
26,62,78 34,43,102 11, 11,?
Pattern: The digits of the first numbers are
interchanged to have the second numbers i.e. “36”
became “63” in the first box.
To get the third numbers in each box the first
number is multiplied by 3.
2. Find out the missing Therefore to get the missing number
number.
11 × 3 = 33
Question 37: B – 29, 21
Steps
1. Define the variables
2. Formulate the equations
Working
Let x = the first number
Let y = the second number
Given the sum of two numbers is 50.
Let these numbers be x and y respectively.
x + y = 50…(1)
“Three times the first is 5 more than twice the
second”
3x = 2y + 5…(2)
Substitute x into the second equation:
3. Make x the subject of the first
equation
4. Substitute x into the second
equation:
5. Expand the brackets
x = 50 – y
6. Solve for x
150 – 3 y = 2y + 5
150 – 5 = 2y + 3y
145 = 5y
145/5 = y
29 = y
x + 29 = 50
x = 21
The numbers are 21 and 29
7. Substitute x back into the
original formula to find y
©"SPECTRUM TUITION PTY LTD
3(50 – y) = 2y + 5
19"
Question 38: D – 300
Steps
1. Find out the original sum of
money.
.
2. Formulate the equation
3. Convert all units to fractions
4. Find the lowest common
denominator (12)
5. Multiply through by 12 to
remove the denominators
Working
Let x be the sum of money that is shared.
Bob, Bill and Phil share out a certain sum of
money amongst them.
Bob gets 2/3 of the sum,
Bill gets 0.25 of the sum and
Phil gets $25
2/3(x) + 0.25 x + 25 = x
0.25 = ¼
2
1
x + x + 25 = x
3
4
×4
2
1 ×3
x+
x + 25 = x "
3
4
8
3
x + x + 25 = x
="
12
12
8x + 3x + 300 = 12x
11x + 300 = 12x
300 = 12x – 11x
300 = x
Question 39: D – 19.2 metres
Steps
1. Find out the length of
material Mrs. Jenkins will
need if her living room has
four double windows.
Working
Given each window panel requires 2 and 2/5
metres of material
The length of material Mrs. Jenkins will need
if her living room has four double windows
= 8 × (2 + 2/5) =
16 + 3 1/5 = 19 1/5 = 19.2
Mrs. Jenkins will need 19.2 metres of
material for her four double windows.
Question 40: A – $2,800.00
Steps
1. Find out the amount Rita was
paid in September for the
work done in the month of
September with option 1
©"SPECTRUM TUITION PTY LTD
Working
There are 4 seven day weeks in the month of
September (28 days in total).
The amount Rita was paid in September for
the work done in the month of September
4 × $700 = $2,800.00
Payment for the last two days for which Rita
worked, she will be paid in October.
20"
Question 41: B – $2142.70
Steps
1. Work out how much money
Rita would have made on the
12th.
2. Work out how much money
Rita would have made on the
16th.
Working
Since it’s her first fortnight, she would be
making $70 for the day.
Since it’s her second fortnight, she would
have received a 10% raise.
$70 + 10/100 x $70
= $70 + $7
= $77
3. Add the two together to find $70 + $77 = $147
out the total.
Rita would lose $147 of potential pay is she
took unpaid days off on the 12th and the 16th.
Question 42: E – None of These
Steps
1. Find out the total amount
received by the national park
in month of July.
Working
Given adult visitors (+18 years) pay a fee of
$5 each, teenagers (13 -18 years) are to pay
$2 each, children (below 13 years) are
charged $1 each and pets attract 20 cents each
before they are allowed entry into the national
park daily.
Adults: 240× $5.00 = $1,200.00
Teenagers: 514 × $2.00 = $1,028.00
Children: 46 × $1 = $46
Pets: 100 × $0.20 = $ 20.00
Total
$2994
2. Find out the total amount Government taxes-10% of daily (by extension
paid by the national park to monthly) takings:
the government as taxes.
10/100 × $2,994 = $299.4
Question 43: D – 16%
Steps
1. Find out the percentage of the
total number of visitors to the
park in July 2011, excluding
pets that were adults.
©"SPECTRUM TUITION PTY LTD
Working
Number of adults: 240
Total number of human visitors:
1500 (240 + 514 + 746)
Percentage of Adult visitors:
(240/1500) × 100 = 16%
21"
Question 44: A –Adults
Steps
1. Find out the category of
visitors that contributed most
to the total takings in July
2011.
Working
Given adult visitors (+18 years) pay a fee of
$5 each, teenagers (13 -18 years) are to pay
$2 each, children (below 13 years) are
charged $1 each and pets attract 20 cents each
before they are allowed entry into the national
park daily.
Adults: 240× $5.00 = $1,200.00
Teenagers: 514 × $2.00 = $1,028.00
Children: 46 × $1.50 = $1,119.00
Pets: 100 × $0.20 = $ 20.00
From the calculations it is clear that adults
contributed most to the total takings in July
2011.
Question 45: A– Plan A
Steps
1. Find out the cheapest option
for the person to send/receive
200 text messages.
Working
Given three plans
A. Unlimited messages for a flat monthly fee$20(sending/receiving)
B. Pay-per-text service- 20 cents per text
message(sending/receiving)
C. 100 free text messages per month
(sending/receiving) and 25 cents per
message charge for any additional
messages.
Cost of Plan A: Flat fee of $20
Cost of Plan B: $0.20 × 200 = $40
Cost of Plan C: $0.25(200 – 100) = $25
Question 46: D– 500
Steps
1. Find out the cheapest option
for the person to send/receive
200 text messages.
©"SPECTRUM TUITION PTY LTD
Working
Let x be that number text messages I need to
send under Plans B and C, such that the cost
of both plans are equal:
Plan B: $0.20 × x
Plan C: $0.25(x – 100)
Equate the two equations together
0.2x = 0.25x – 25
25 = 0.05x
25/0.05 = x
500 = x
22"
Question 47: A – 8
Steps
1. Define the variables
Working
Let r = the amount that Robert has and
l = the amount that Lizzy has:
2. Formulate the equations
r + 4 = 6l….. (1)
r – 6 = l……. (2)
3. Using Substitution:
Substitute equation 2 into equation 1
and solve for unknown i.e. r
r + 4 = 6(r –6)
r + 4 = 6r – 36
36 + 4 = 6r – r
40 = 5r
r = 40/5
r=8
Question 48: A - Ron
The phrase "least variety of marbles" must be taken to mean different colours. Clearly
the answer is Ron, as he has blue and red marbles only, while the others have green
marbles as well. No arithmetic is needed for that.
Question 49: A – Ron
Now, as we only know the relative value of the marbles, we can make things easier
by assuming that a red marble will cost $2,a blue marble will be worth $1(blue
marbles will fetch half of the price of red ones at auction),and a green marble will be
worth $0.5(green will fetch a quarter)
Mark has (30 × $1) + (20 × $2) + (10 × $0.5) = $75 worth.
Ron has (80 × $1) + (10 × $2) = $100 worth.
Derrick has (40 × $1) + (10 × $2) + (30 × $0.5) = $75 worth.
Mr. Marblesman has a quarter of what Ron has ($25 worth), plus ten of each
(10 x $1 + 10 x $2 + 10 x $ 0.5 = $35) for a total of $60.
So the most valuable collection is Ron's.
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23"
Question 50: D – 1200km
Steps
1. Define the variables
Working
Let x represent the unknown distance that
the same car can cover on a full tank.
2. Find the ratio statement
The ratio statement is:
!"#!!"
!!!"#$%&
3. Determine the proportions
!"#!!"
4. Solve for x by cross multiplying
fractions:
!"#
!!!"#$%&
!
!!!"
= !"!!"#$%&
!
= !"
6x = 120 × 60
6x = 7200
x = 7200/6
x = 1200
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
©"SPECTRUM TUITION PTY LTD
24"
VERBAL REASONING
EXAM PAPER 1
Detailed Solutions
"
Question 1: D - honour
To recall means to remember and show respect for something, as does honour, so the
answer is D.
Option A: Sympathise means to feel sorry for someone’s situation.
Option B: Party means to celebrate.
Option C: Continue means to keep doing something.
Question 2: B - avoidable
Inevitable is an adjective to describe something that can’t be prevented or avoided.
Avoidable is the opposite of this.
Option A: Empty means to not contain anything.
Option C: Enviable is an adjective to describe something you might be envious of.
Option D: Regrettable is an adjective to describe something that you might regret.
Question 3: A - Cousin
The best way to answer these questions is to draw a family tree.
Marg
Claire
Glenn
Me
Jacqui
(Brothers)
Oiver
Gary
Lily
Claire and Lily are cousins, as their fathers are brothers.
Question 4: A – 163
Jeremy is 180cm tall.
Kyra is 20cm shorter than this, so she is 160cm tall.
Therefore, Paul’s height is taller than 160cm and shorter than 180cm.
The only possible answer is A, 163cm.
Question 5: A - Adjective
An anagram of LISTEN is SILENT, which is an adjective that means quiet.
©"SPECTRUM TUITION PTY LTD
25"
Question 6: A – A place full of flowers and trees.
The anagram of DANGERS is GARDEN, which is a place full of flowers and tress.
Question 7: B – 8 metres
Use a map to figure out where each ball landed.
North
B
O ! ! ! X
R
From this, we can see that the red and orange balls are 8 metres apart.
Question 8: C - thoughtless
Considerate is an adjective that means thoughtful and caring, which is the opposite of
thoughtless.
Option A: Attentive is a synonym to considerate.
Option B: Patient means tolerant of delays.
Option D: Accomodating means welcoming.
Question 9: A - dooclova
Baba
Glaba
Doo
Must mean kind, as it appears words 1 and 2
Must mean car, as it appears in words 1 and 3
Must mean very, as we know that baba means kind
The phrase ‘very cool’ must include doo. Note that the order of words is the same as
in English, i.e., the adjective comes before the noun. In the list of possible answers,
dooclova is the only doo word that follows this pattern.
Question 10: B - Paris
Melbourne is a city in Australia. Paris is a city in France.
Question 11: B – Some tables are glables
You can answer this question using a Venn diagram.
No rables are driks = False
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26"
Some tables are glables = True "
All fables are rables = False
No rables are glables = False
Question 12: C - Emperor
A king is the ruler of a kingdom. An emperor is the rules of an emperor.
Question 13: B – My car weighs a tonne.
A is hyperbole, as the speaker is probably not literally starving, they are just hungry.
C is hyperbole, as the speaker’s boss probably won’t actually kill the speaker.
D is hyperbole as the person’s eyes are probably not actually as bright as the sun.
B is probably not hyperbole, as cars actually do weigh about a tonne.
Question 14: D – pyramid
Rectangle, octagon and circle are all the names of two-dimensional shapes. A
pyramid, on the other hand, is a three-dimensional shape.
Question 15: D - rib
Root, stem and bud are all parts of plants. However, a rib is a part of an animal.
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27"
Question 16: A - apathetic
The word concerned means worried or caring, which is the opposite of apathetic,
which means uncaring.
Option B: Bothered means concerned.
Option C: Troubled also means concerned.
Option D: Considerate means caring.
Question 17: C – Ruby
Create a quick table and fill it out as you read through the information given.
Drums
Bass Guitar
Electric
Guitar
Singing
Laura
Chris
Shaun
Ruby
Laura plays an instrument with strings, so she doesn’t play drums or sing.
Drums
Laura
Chris
Shaun
Ruby
Bass Guitar
Electric
Guitar
✕
Singing
✕
The drummer has the same amount of letters in their name as the guitarist. Shaun is
the guitarist. Shaun has 5 letters in his name, so the drummer must have 5 letters in
their name. Laura isn’t the drummer, so Chris must be the drummer.
Drums
Laura
Chris
Shaun
Ruby
✕
✓
✕
✕
Bass Guitar
✕
✕
Electric
Guitar
Singing
✕
✕
✓
✕
✕
✕
✕
As we can see, the only person who could be the singer is Ruby.
Question 18: A – 3
There are 5 capitalised vowels: A, E, I, O and U.
Of these, only I, O and U can be written using a single line.
A would require 3 lines and E would require 4 lines.
©"SPECTRUM TUITION PTY LTD
28"
Question 19: D - adore
Detest is a verb that means strongly dislike, which is the opposite of adore.
Option A: Admiration seems like the opposite of detest, but it is a noun, while detest
is a verb.
Option B: Hatred is also a noun, and its meaning is similar to detest.
Option C: Beloved seems like the opposite of detest, but it is an adjective, while
detest is a verb.
Question 20: A - Amused
People feel frightened when they watch horror movies. People feel amused when they
watch comedy movies. Therefore, frightened is to horror as amused is to comedy.
Question 21: B – TAKES
We start with the letters
SKATE
We switch the first and last letter to get
EKATS
Then I switch the second and fourth letter to get
ETAKS
Finally, I take the first letter in the line and put it before the final letter to get
TAKES
Question 22: C – 6:40
First, work out how long the trip usually takes.
5:20 – 4:00 = 1:20
So if it usually takes 1 hour and 20 minutes, today it will take 2 hours and 40 minutes.
So I will get home at 4:00 + 2:40 = 6:40.
Question 23: A – 5
You can make 4 other 4-letter words from the letters of SATE. These are EAST,
EATS, SEAT, TASE and TEAS.
Question 24: C - meager
Lavish is an adjective that means fancy or luxurious, which is the opposite to meager,
which is an adjective that means lacking in quality. All of the other words are
synonyms to lavish.
Question 25: D - admiration
Detest, respect and hate are all verbs that describe attitudes or emotion. Admiration,
on the other hand, is a noun.
©"SPECTRUM TUITION PTY LTD
29"
Question 26: D - Dunden
As you get new information, put the mountains in order. Firstly, we know that Mount
Barklay is taller than Mount Dunden and Mount Fraser. At this stage, we don’t know
whether Mount Dunden or Mount Fraser are taller.
Barklay
Dunden – Fraser
We then learn that Mount Noodle is taller than Mount Fraser but shorter than the rest
of the mountains.
Barklay
Dunden
Noodle
Fraser
From this, we can see that Mount Dunden is the second tallest mountain.
Question 27: A – Dancing, I , is
CLOVER
BLAN
GREEV
SEEP
and
FOOF
Must mean dancing, as it is in sentence 1 & 2
Must mean hate, as it is in sentence 1 & 3
Must mean I, as it is the only remaining word in sentence 1
Must mean is and dangerous, since they are both is sentence 2 and 3.
So CLOVER, GREEV, SEEP could mean DANCING, I and IS or DANCING, I and
DANGEROUS. The only answer that fits these possibilities is A.
Question 28: D - say
Rain is a less extreme version of pour. Say is a less extreme version of scream.
Therefore, rain is to pour as say is to scream.
©"SPECTRUM TUITION PTY LTD
30"
Question 29: B – Linda, Jeremy, Sammy
Create a diagram based on the information given.
From this, we can see that Linda is closest to Clive, at distance of 2 miles. Jeremy is
the second closes, at 3 miles away. We would have to use trigonometry to work out
exactly how far away Sammy is, but for the purpose of this question, we can simply
tell that she is the furthest away.
Question 30: A – 1 step
Use a diagram to track the movement of the robot. It doesn’t matter what direction to
the robot starts in. In this example, it takes 1 step east, turns left to the north, moves 1
step, turns left to the west, moves 2 steps, turns left to the south and takes 1 step.
!
# End
!
Start
"
$
At the end of the journey, the robot is 1 step away from its starting position.
©"SPECTRUM TUITION PTY LTD
31"
Question 31: D – I have more red fruit than yellow fruit
Make a list of each type of fruit that I have.
Apples: 1 green + 2 red = 3
Cherries: 3
Bananas: 4
Round fruit: 3 apples + 3 red cherries = 6
Red fruit 2 apples + 3 cherries = 5
Green fruit: 1
Yellow fruit: 4
Based on this information, the only accurate statement is that I have more red fruit (5)
than yellow fruit (4).
Question 32: B – No GOPS are PROFS
Use a Venn diagram to work out the answer.
As we can see, A is incorrect because only some SALAZES are JEELS.
C is incorrect as some GOPS are JEELS.
D is incorrect. Some PRODS could be JEELS. But all we know about PRODS is that
no PRODS are GOPS. Therefore, we don’t know for sure that some PRODS are
JEELS.
We do know, however, that no GOPS are PRODS.
Question 33: A - run
Howl, blow and gust are all verbs that can describe what the wind does. The wind
does not run.
©"SPECTRUM TUITION PTY LTD
32"
Question 34: C - type
Sort, kind and class are all words that mean category or type. Therefore, type fits on
this list.
Question 35: B - ballad
Waltz is a type of dance. Ballad is a type of song. Therefore, dance is to waltz as song
is to ballad.
Question 36: D - Even though Mrs. Nguyen failed her first test, she quickly got
back to studying for the next test.
Resilient is an adjective to describe someone who doesn’t give up when faced with
difficulties. Of all the answers, only D provides a situation in which Mrs. Nguyen
faced a setback and didn’t give up.
Question 37: D – potter
Smith, tailor and baker are all occupations that can also be surnames. Potter is also an
occupation that can be a surname.
Question 38: D – Lions
As you get new information, put the animals in order. Firstly, we know that dragons
are bigger than lions.
Dragons
Lions
Next, we know that bears are bigger than lions and tigers. However, we don’t yet
know whether lions or tigers are bigger.
Dragons
Bears
Lions – Tigers
Finally, we learn that tigers are bigger than cheetahs but smaller than lions.
Dragons
Bears
Lions
Tigers
Cheetahs
By looking at the list, we can tell that lions are the third biggest animal.
©"SPECTRUM TUITION PTY LTD
33"
Question 39: D - pack
Solve, crack and decipher are all verbs that mean to solve a tricky puzzle or problem.
Pack is the odd word out.
Question 40: C - shake
Brandish is a verb that means to wave or flourish an object in the air. The nearest to
this meaning is shake.
Question 41: A - love
If I am furious, I am feeling anger. If I am besotted, I am feeling love. Therefore,
furious is to anger as besotted is to love.
Question 42: D – 1 and 5
As per statement 1, when I don’t remember something, I write it on the back of my
hand. According to statement 5, my phone number is written on the back of my hand.
This must mean that I don’t remember my phone number.
Question 43: B – Painful.
Agony, torment and horror are all nouns that describe a painful or terrible experience.
Torture, suffering and anguish are also nouns that describe painful or terrible
experiences. Painful is an adjective, so it does not fit on this list.
Question 44: A - ropable
Affable, sociable and likeable are all adjectives to describe a friendly person. Ropable
is an adjective to describe someone who is annoyed.
©"SPECTRUM TUITION PTY LTD
34"
Question 45: C - Tony
Draw up a table and fill it out as you get more information.
Chef
Waiter
Manager
Leo
Chris
Tony
If Chris plays footy with the chef, then Chris is not the chef.
Chef
Leo
Chris
Tony
Waiter
Manager
✕
If Leo and the waiter are best friends, then Leo is not the waiter.
Chef
Leo
Chris
Tony
Waiter
Manager
✕
✕
If Chris is the manager, then Tony must be the waiter.
Leo
Chris
Tony
Chef
Waiter
Manager
✕
✕
✕
✓
✓
Question 46: E – None of the statements is a known fact
Statements I, II and III cannot be deduced from Facts 1, 2 and 3. Therefore none of
the statements is a known fact.
Question 47: B - False
Using a diagram to decide on the location of the towns, it becomes clear that Canberra
is south of Cairns, not northwest.
©"SPECTRUM TUITION PTY LTD
35"
Question 48: A – No BIGS can be ZIGS
Use a Venn diagram to work out the answer.
As we can see, A is correct. All we know about ZIGS is that no ZIGS are PIGS. This
doesn’t mean that ZIGS can’t overlap with FIGS and BIGS. Therefore, it is incorrect
to say that no BIGS can be ZIGS.
Question 49: A - bitter
Abrupt is the opposite of long. Sweet is the opposite of bitter. Therefore, sweet is to
bitter as abrupt is to long.
Question 50: D - rant
This is a tricky one, because rage can be a noun that means anger. For example “I am
full of rage.” But it can also be a verb that means to express anger. For example “I am
going to rage at the vandals if I catch them.” Rant is also a verb that means to express
anger.
Question 51: C - I and II only
I. All black cats have tails (Fact 2), but only some animals are cats (Fact 3).
Therefore, some black animals, which aren’t cats, could have no tails.
II. We know that there are black cats (Fact 2). And we know that these black cats are
animals (Fact 3). Therefore, there are at least some black animals.
III. We know that all black cats have tails (Fact 2). Therefore, statement III must be
false.
©"SPECTRUM TUITION PTY LTD
36"
Question 52: A - True
If Annie has less money than Jenna, but more money than Katie, then the order of the
girls from least to most money is Katie, Annie, Jenna. Therefore, Katie does indeed
have the least amount of money.
Question 53: A - True
If Snikes have webbed feet (statement 1) and no flightless bird has webbed feet
(statement 2), then Snikes can’t be flightless. Therefore, the third statement is true.
Question 54: B - burngeek
geek
lasso
leeper
burn or seem
Must mean blue, as it appears in 1 & 3
Must mean car, as in 1
Must mean baby, as in 3
Must mean bell, as in 2.
The only answer with ‘geek’ (blue) and either ‘burn’ or ‘seem’ is B.
Question 55: A - Kelly’s friend is sad about failing a test. Kelly tells her friend
that lots of people found the test really easy.
In answer A, Kelly tells her friend that lots of people found the test really easy. This
will make Kelly’s friend even sadder about failing the test. This is exacerbating her
sadness. None of the other solutions involve Kelly making an already bad situation
worse.
Question 56: A - Mika
The best way to answer these questions is through a table. We only know the names
of two of the friends. But, as we will see, this does not matter in the end.
Flu
Chickenpox
Rash
Mika
Laura
Unknown friend
First, we learn that Mika and Laura visit the friend with chickenpox. This means that
the unknown friend must be the one with chickenpox.
Mika
Laura
Unknown friend
Flu
Chickenpox
✕
✕
✕
✓
Rash
✕
We then learn that the person with the rash got it while helping Laura and her mother.
This means that it isn’t Laura. Therefore, Mika must have the rash.
©"SPECTRUM TUITION PTY LTD
37"
Mika
Laura
Unknown friend
Flu
Chickenpox
✕
✓
✕
✕
✕
✓
Rash
✓
✕
✕
Question 57: A - Grandfather
The word paternal refers to the father’s side of the family.
Jeremy’s father’s paternal grandmother is Jeremy’s father’s father’s mother, or
Jeremy’s great grandmother. Her only son is Jeremy’s grandfather.
Question 58: C - ditch
Trough, channel and gully are all words to describe types of holes or openings in the
ground. Ditch is also a word for a hole in the ground.
Question 59: D - owl
People often refer to foxes as sneaky. People often refer to owls as wise. Therefore,
sneaky is to fox as wise is to owl.
Question 60: D - Berate
Titter, chuckle, and guffaw are all verbs to describe laughter. Moan, on the other hand
is a sound not related to laughter.
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
©"SPECTRUM TUITION PTY LTD
38"
SELECTIVE MATHEMATICS
TEST 1
Worked Solutions
!
!
Question 1.B. $5,612.82 AUD
Convert $5,500 to AUD. Use the equivalence 1AUD = $ 0.9799 US.
To convert, multiply $5,500 by
$5, 500 ×
1AUD
to cancel the dollar sign. So we have:
$0.9799
1AUD
= $5, 612.82 AUD
$0.9799
Therefore, Steven received $5,612.82 AUD.
Question 2.A. $1,469.85
Convert 1,500 AUD back to USD. Again, use the equivalence: 1AUD = $ 0.9799 US.
$0.9799
To convert, multiply 1,500 AUD by
to cancel AUD sign. So we have:
1AUD
$0.9799
1,500 AUD ×
= $ 1469.85
1AUD
Therefore, Steven received $1,469.85.
Question 3.A. 224w
Volume of a rectangular prism is defined by the formula: V = lwh
V = 16 (w) (14) = 224w
©"SPECTRUM TUITION PTY LTD
39"
Question 4.B. 8.84 metres
Get the volume of the 20 small boxes then equate it to the volume of the storage
room.
But first, convert each dimension of the 20 small boxes into feet by multiplying
the equivalence,
1 metre
to cancel out centimetres.
100 centimetres
Hence,
1 metre
= 6 metres
100 centimetres
1 metre
550 centimetres inches ×
= 5.5 metres
100 centimetres
1 metre
300 centimetres ×
= 3 metres
100 centimetres
600 centimetres ×
Volume of 1 small box = (6 m) (5.5 m)(3 m) = 99 cubic metres
Volume of 20 small boxes = 99 cubic metres (20) = 1,980 cubic metres
Volume of the storage room = Volume of 20 small boxes
224 w = 1980m3
224 w 1980m3
=
224
224
w = 8.84m
Therefore, the width of the storage room is 8.84 metres.
Question 5.A. x < 1
Solve the inequality:
5 − 2 x ≤ 6 − 3x
−2 x + 3x ≤ 6 − 5
x ≤1
©"SPECTRUM TUITION PTY LTD
40"
Question 6.E. 30 degrees
As the question states, ∠CAD = 120° . Because the sides AC and AD are both
equal to the radius of the circle, then the triangle ACD is isosceles, which means
that
∠BCD = ∠CDA
180 = 120 + 2∠BCD
Therefore
2∠BCD = 60
∠BCD = 30°
"
!
30°
120°
30°
!
Question 7.C. 90 degrees
Because" ∠CAD "and" ∠DAB "forms"a"straight"line,"we"can"say"that."
120° + ∠DAB = 180°
"
∠DAB = 60°
Because"AB"and"AB"are"the"same"length"(the"length"of"the"radius),"then"we"know"that"
∠ADB = ∠ABD
180 = 60 + 2∠ADB
2∠ADB = 120
∠ADB = 60°
"
"
If" ∠ADB = 60° "and" ∠CDA = 30° "
Then" ∠CDB = 30° + 60° = 90° "
©"SPECTRUM TUITION PTY LTD
41"
120°
60°
30°
60°
60°
"
Question 8.A. 30 degrees
Because EDF is a tangent to the circle, we know that the angle of ∠ADF = 90°
We already know that ∠ADB = 60° , so we can say that
∠BDF = 90° − 60° = 30°
120°
60°
60°
30°
30°
©"SPECTRUM TUITION PTY LTD
60°
42"
Question 9.E. 18
The sum of the exterior angles of any polygon is always equal to 360 degrees. A
polygon is regular if and only if all its sides and interior angles are equal. Since an
interior and exterior angles of a polygon are supplementary and all interior angles of a
regular polygon are congruent, then al exterior angles as well are congruent. Hence,
the degree measure of each exterior angle of a regular polygon can be found by
dividing 3600 by the number of sides, n.
360 0
n
360 0
n=
200
n = 18
200 =
Question 10. D. 81
Based on the information displayed in the graph, the number of movie goers who
favoured action movies is 27% of the total number of movie goers surveyed.
Favoured action movies = 27% (300) = 81
Question 11.D. 15%
To find the percentage of movie goers who favoured science-fiction, add the
percentages of movie goers who favoured the other types of movies then subtract
from 100%. Since the number of movie goers who favoured comedy is not known, we
need to solve it first. Do this, by dividing the degree measure of the sector that
represents comedy by 360 degrees.
30% + 27% + 13% + 15% + science fiction = 100%
85% + science fiction = 100%
science fiction = 100% – 85%
science fiction = 15%
Therefore, 15% of the sector represents science-fiction.
Question 12. E. None of these
To find the percentage of the sector that represents comedy, drama and romance, we
add those percentages together.
30% + 15% + 15% = 60%
©"SPECTRUM TUITION PTY LTD
43"
Question 13.D. 46.80
Steps
Working
To find the degree measure of the sector
that represents Romance, get 13% of the
degree measure of one whole rotation
(circle). Since 1 complete rotation (circle)
is equal to 360 degrees, we multiply 13%
and 360 degrees
Convert the percentage to a decimal and
0.13 x 360 = 46.8o
multiply by 360
Question 14.E. 2,750
The numbers of new homes built in New Homes in City Ville from 1981 to 1990
and from 1961 to 1970 are represented by this pictogram:
Since each
represents 500 homes, multiply the number of
by 500.
Number of new homes built from 1961 to 1970 = 9.5(500) = 4,750
Number of new homes built from 1981 to 1990 = 15(500) = 7,500
Difference =
2,750
Question 15.C. 0.625 hour
Steps
1. Consider the formula to calculate
distance
2. Plug-in these values to the distance
formula above and solve for time.
©"SPECTRUM TUITION PTY LTD
Working
Distance = Rate × time
Given:
Distance = 25 km
Rate = 40 km/h
Distance = Rate × time
40km
25km =
× time
1hr
25 km
time =
40 km
1 hr
1 hr
time = 25 km ×
40 km
time = 25 / 40 hr
time = 0.625 hour
44"
Question 16.E. 40 km/h
Steps
1. Consider the formula to calculate
speed
2. Plug in the values
Working
Distance = Rate × time
Given:
Distance = 20 km
Time = 30 minutes
Plug-in these values to the distance
formula above and solve for rate.
Distance = Rate × time
20 km = rate × 30 min .
20 km = rate × 30 min . ×
1 hr
60 min .
20 km = rate × 0.5 hour
20 km
= rate
0.5 hour
rate = 40 km / h
Question 17.B. 4
The perimeter of a triangle refers to the sum of the lengths of its sides.
Given:
Side 1 = a + 2
Side 2 = a + 4
Side 3 = a + 6
Perimeter = 24 cm
Perimeter = side 1 + side 2 + side 3
24 = (a + 2) + (a + 4) + (a + 6)
24 = 3a + 12
24 – 12 = 3a
12 = 3a
a=4
©"SPECTRUM TUITION PTY LTD
45"
Question 18. A - 12.96
WY is the base of right triangle XWY . To find the length of WY, we first find
the lengths of XW and XY, respectively.
XW = a + 0.8 = 4 + 0.8 = 4.8
XY = a + 2 = 4 + 2 = 6
Use Pythagoras’ theorem to solve for the length of WY.
XY2 = XW2 + WY2
62 = 4.82 + WY2
WY2 = 62 – 4.82
WY2 = 36 – 23.04
WY2 = 12.96
WY =
12.96
Question 19.D. 24 cm2
To find the area of triangle XYZ, we may either use the lengths of sides XZ and
XY or XW and ZY. The results would be the same.
Preferably using XZ as the height and XY as the base of right triangle XYZ, we
compute the area as follows:
Area = ½ bh
= ½ (a + 4)(a + 2)
= ½ (4 + 4)(4 + 2) Plug-in the value of a
= ½ (8)(6)
Area = 24 cm2
Question 20.C. 18 cm
To find the length of each side of the cubic box, get the sum of the lengths of the
diameter of each circular base of the three tangent cans that are aligned along each
side of the box.
Length of diameter of 1 circular base = 2 (length of the radius)
= 2 (3 cm)
= 6 cm
Sum of the lengths of the diameters of 3 tangent circular bases = 3(6 cm) = 18 cm
Length of each side of the cubic box = Sum of lengths of the diameters of 3 tangent
cans
Each side of the cubic box has a length of 18 cm.
©"SPECTRUM TUITION PTY LTD
46"
Question 21.E. 69.5304 cm2
Compute the areas of each upper base of the 9 cans and subtract it from the area of the
base of the cubic box. Use the following area formulas:
Area of a square = s2 where s is the length of each equal side or length x width
Area of a circle = πr2 where r is the length of the radius
Area of the base of the box = (18 cm)2 = 324 cm2
Total area of the upper bases of 9 cans = 9π(3 cm)2
= 9(3.1416)(9 cm2)
= 28.2744 x 9
= 254.4696 cm2
Area of the region NOT occupied by the cans
= 324cm2 – 254.4696 cm2 = 69.5304 cm2
Question 22. D. 54 cans
Each box contains 9 cans of milk.
Total cans of milk contained in 6 boxes = 9 cans (6) = 54 cans
Question 23. B. t = - 1
Rewrite each number in scientific notation back to the standard form. Perform the
operations involved and solve for t.
(
)(
)
4
−3
Given: 4.2 ×10 3 ×10 = 1, 000
1.26 ×10t
Solution:
42000 ( 0.003)
= 1000
1.26 ×10t
126
= 1000
1.26 ×10t
126
= 1.26 ×10t
1000
0.126 = 1.26 ×10t
0.126 1.26 ×10t
=
1.26
1.26
t
0.1 = 10
10−1 = 10t
∴ t = −1
©"SPECTRUM TUITION PTY LTD
47"
Question 24. A. r =!
!!!
!"
Manipulate the given equation and solve for r.
Given: A = P + Pr t
Solution:
A = P + Pr t
A − P = Pr t
A − P Pr t
=
Pt
Pt
A− P
=r
Pt
A− P
∴r =
Pt
Question 25.C. 3
Find the number of pupils who only have cats as pet and those who have dogs
and birds as pets only.
Number of pupils who only have cats = 13 – (4 + n) = 9 – n
Number of pupils who have dogs and birds only
= 19 – (5 + n + 4) = 19 – 9 – n = 10 – n
Add the number of elements for each of the 6 regions including the region
outside the 3 circles and equate the sum to the total number of pupils surveyed.
5 + 5 + (10 – n) + n + 4 + (9 – n) = 30
5 + 5 + 10 – n + n + 4 + 9 – n = 30
33 – n = 30
– n = 30 – 33
n=3
There were 3 fifth grade pupils who have all three kinds of pets.
©"SPECTRUM TUITION PTY LTD
48"
Question 26. D. 14
At least two means two or more. Find the number of pupils who have two or three
kinds of pets:
Dogs and Birds
Dogs and Cats
Dogs, Birds and Cats
Total
=7
=4
=3
= 14
Question 27. B. 11
Add the number of pupils who have cats only or those who have dogs only.
Number of pupils who have cats only = 9 – n = 9 – 3 = 6
Number of pupils who have dogs only
=5
Total = 11
Question 28.B. 4x + 6y = 12
Parallel lines have equal slopes.
Write each equation in slope intercept form and identify which equation has the
same slope as 2x + 3y = 8.
First, rewrite 2x + 3y = 8 into the form y = mx + b. Then, write each equation in A
through E into the same form.
2x + 3y = 8
A. x = y – 3
B. 4x + 6y = 12
3y = -2x + 8
y = -2/3 x + 8/3
m = -2/3
y = x + 3, m = 1
6y = -4x + 12
y = -2/3 x + 2, m = -2/3
As found, the equation in B has the same slope as the given equation. You may or
may not proceed to choices C through E.
Thus, the line defined by the equation, 4x + 6y = 12 is parallel to the line defined
by the equation 2x + 3y = 8.
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49"
Question 29. D. 16
Use the equation below to solve for the value of a, b and c.
⎡ a ⎤ ⎡ 2⎤
⎢ 2b ⎥ = ⎢ 4 ⎥
⎢⎣3c ⎥⎦ ⎢⎣1 ⎥⎦
From this equation, we have:
a=2
2b = 4 so b = 2
3c = 1 so c = 1/3
Plug-in the value of a, b and c to the expression, 2a b + 3ab − 12c and simplify.
2(2)2 + 3(2)(2) – 12(1/3) = 8 + 12 – 4 = 16
Question 30.A. 0.005832 cubic metres
Find the length of each side of the cube. Use the given base areas. Recall that a
cube has 2 square bases, each with an area equal to the square of the length of
each side, A = s2.
Total base areas = 648 cm2
Total base areas = 2s2 = 648 cm2
s2 = 324 cm
s = 18 cm
Convert 18 cm to metres. Multiply this with the equivalence
1m
to cancel out cm
100cm
unit.
18 cm ×
1m
= 0.18m
100cm
Volume of a cube = s3
Volume of the cubic box = (0.18m)3 = 0.005832 m3
Question 31.C. III only
Since x is larger than 21, the ordered array remains the same. The median for this
data set is the middlemost value, which is 15.
7, 9, 14, 15, 19, 21, x
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50"
Question 32. B. $1.67
Equate the given equation for p to 1 and solve for the value(s) of t.
Steps
Working
1 The first step is to find the proceeds at a p(1) = 0
ticket price of $1.
2. Next, we determine at which value of t p(t) = p(1) = 0 = -3t2 + 8t - 5
the proceeds are the same as when the
value of t is $1.
3. Next, we apply the quadratic formula
−b ± b 2 − 4ac
2
as the function is in the form ax + bx + c
2a
to solve for t.
4. When a = -3, b = 8 and c = -5, plug in
−8 ± 8 2 − (4 × −3 × −5)
the values into the quadratic formula
2 × −3
−8 ± 64 − (60)
=
−6
−8 ± 4
=
−6
−8 ± 2
=
−6
−8 + 2
−8 − 2
=
or
−6
−6
−6
−10
=
or
−6
−6
5
1 or
3
=$1.67
Question 33.C. 0
Solving the equation algebraically will lead to the cancellation of variable x.
x+x+x+x+x = x
5x = x
Hence, the only value of x that can make the equation true is x = 0.
5(0) = 0, true
Question 34.D. 6
Set A is a set of all numbers that are either less than –15 or greater than 5. This
statement can be translated into: A= ( −∞, −15) ∪ (5, ∞ ) .
Among the given numbers, only 6 belongs to set A. The rest belong to the
complement of A, which means that things are not in (that is, outside of) A.
©"SPECTRUM TUITION PTY LTD
51"
Question 35.D. 5
Volume of a cylinder = πr2h
Volume of cylinder B = 3× Volume of cylinder
πr2 (15) = 3× πr2h
15 = 3h
dividing both sides by πr2
h=5
dividing both sides by 3
Question 36.D. 15
This question involves the application of lowest common multiple (LCM).
Multiply 3 and 5 to get 15. The phone and the horn will sound in sync after 15
minutes.
Multiples of 3 = 3, 6, 9, 12, 15
Multiples of 5 = 5, 10, 15
Question 37.D. 18
Simplify the equation 3x 2 + 6m = 54 by dividing both sides by 3 and get x2 + 2m on
the left side.
3 x 2 6m 54
+
=
3
3
3
2
x + 2m = 18
Thus, the value of x2 + 2m is 18.
Question 38.E. x2 + z2 = y2
Choices A and C are incorrect. The length of the hypotenuse of right triangle is
always greater than the length of each leg. Choice B would only be true unless the
dimensions of the legs are known. Nonetheless, choice E is always true since this
supports the “Pythagoras theorem” that states “In a right triangle, the sum of the
square of the lengths of the legs is equal to the square of the length of the
hypotenuse”. Choice D uses a wrong equation.
The correct answer is E.
Question 39. C. April 1
Kevin’s automobile guidebook states that the oil in his car must be changed every
3 months or every 3,500 kilometres it had driven, whichever occurs first. Since he
had the oil changed on January 1, then he should change it again either on April 1,
which is 3 months after January 1 or if his car had travelled 14,000 kilometres
(10,500 + 3,500), whichever comes first.
Based from the information in the table, Kevin had driven his car for 14,000
kilometres until May 1. So April 1 comes first.
©"SPECTRUM TUITION PTY LTD
52"
Question 40. C. 995 kilometres
Subtract the cumulative distances for May 1 and April 1 to find the distance for the
whole month of April.
Cumulative Distance on May 1 = 14,000 km
Cumulative Distance on April 1 = 13,005 km
Difference = 995 kilometres
Question 41. A. 1, 1, 2, 2, 3, 3, 3
Mode refers to the most frequently occurring value(s) in a data set. The mean
(arithmetic average) of a set of data is found by adding all the data values then
dividing the sum by the number of data points.
Get the mode and mean of each data set and compare. Identify the data set that has
a mode greater than the mean.
A. 1, 1, 2, 2, 3, 3, 3
Mode = 3
Mean = 15/7 = 2.14
B. 1, 2, 2, 2, 3, 4, 5
Mode = 2
Mean = 19/7 = 2.71
C. 1, 1, 1, 1, 3, 3, 4, 6
Mode = 1
Mean = 20/7 = 2.86
D. 2, 2, 3, 3, 3, 4, 5
Mode = 3
Mean = 22/7 = 3.14
E. 1, 2, 2, 3, 4, 5, 6
Mode = 2
Mean = 23/7 = 3.29
The data set in A satisfies the given condition regarding the mode and the mean.
©"SPECTRUM TUITION PTY LTD
53"
Question 42. D. 4.5 2 (approximately 6.36) square units
Steps
1. Find the length of CD
Working
Since the area of square ABCD is 81
square units, then the length of each side
must be equal to 9 units.
Area of a square = s2
81 = s2
s=9
Based on the diagram, side CD of ABCD
is a diagonal of square EDFC and at the
same time a hypotenuse of right triangle
CED.
2. As CD is 9 units, halving it will be
equal to 4.5 units. The length we need to
find will therefore be the hypotenuse EC.
4.5"
3. Use Pythagoras’ theorem to find the
length EC
a2 + b2 = c2
4.52 + 4.52 = EC2
EC = 4.5 2 + 4.5 2
EC = 4.5 2
Question 43. C. w = 3 × 2a −1
If a = 1, then w = 3 = 3 = 3 × 20
If a = 2, then w = 6 = 3 × 2 = 3 × 21.
If a = 3, then w = 12 = 3 × 2 × 2 = 3 × 22.
If a = 4, then w = 24 = 3 × 2 × 2 × 2 = 3 × 23.
Note that the value of w for a given value of a can be expressed into the form
3 × 2a – 1. Hence, w = 3 × 2a – 1 .
©"SPECTRUM TUITION PTY LTD
54"
Question 44. D. 96 kg
Use the equation w = 3 × 2a – 1. Replace the variable a with 6 and solve for w.
w = 3 × 26 – 1 = 96.
Question 45. A. 7 months
Use the equation w = 3 × 2a – 1. Replace the variable w with 192 and solve for a.
192 = 3 × 2a – 1
192/3 = 2a – 1
64 = 2a – 1
26 = 2 a – 1
6=a–1
a=7
Question 46. E. 6
Any parabola is symmetrical with respect to its line of symmetry, the line through the
vertex. Since the graph of f is symmetrical with respect to x = 1, then we can say that
points (-2, p) and (4, 6) are equidistant (the same distance) from x = 1 and that one is a
reflection of the other. So they must have the same coordinate. Thus, p = 6.
Question 47. D. 4
Steps
1. Use the slope formula (gradient) for a
line.
Working
2. Substitute the given two points and the
slope.
Given: (-2, p), (-3, k) and slope = 2
k− p
2=
−3 − (−2)
3. Solve for k
Formula: m =
y2 − y1
x2 − x1
k−6
−3 + 2
k−6
2=
−1
−2 = k − 6
2=
4=k
Question 48. A. 10
Since ΔEBD is equiangular, then it must also be equilateral.
As such, EB = BD = ED = 10.
Given: ED = 10
©"SPECTRUM TUITION PTY LTD
55"
Question 49. D. 30
The perimeter of an equilateral triangle is equal to three times the length of each leg.
P = 3s = 3(10) = 30
Question 50. B. 30
5! 36 = ?
!"! 36 ! = !! 6! !! = !!6"
As the square root can be simplified, move the 6 outside the square root
!ℎ!"!#$"!!!5×6"
!"#$%&#'!5!!"#!6!!"#$!ℎ!"."
5×6! = !!30:"
!"#$%&:!30"
Question 51. E None of the above.
Steps
1. Write the given equation. The answers
give us a clue that we will likely be
completing the square, also note that
there is an xy term and 4 is a square
number.
2. To complete the square we need to
halve the coefficient of the x term, 2y.
3. This must then be added to both sides
of our equation.
4. We can now simply the left hand side
(LHS) of the equation using the rule
(a+b)2=a2+2ab+b2. in our case, a=x and
b=y.
5. We can also simplify the right hand
side (RHS) of the equation using the
difference of two squares, a2-b2=(a+b)(ab). Note that a=y and b=2.
6. we can not bring the simplified LHS
and RHS together.
7. To find the value of x+y, which is
common amongst 3 of the possible
answers, we need to take the square root
of both sides to remove the squared from
x+y
8. The answer was E. The answer A is
incorrect as there is not square root sign.
Note that the answer B would trick a
student who was not careful with their
minus signs. Answer C would trick a
student who forgot to take the square root
correctly. D has x-y, not x+y.
©"SPECTRUM TUITION PTY LTD
Working
x2 + 2xy = -4
2y/2=y
(x)2 + 2(x)(y) + (y)2 = -4+(y)2
(x)2 + 2(x)(y) + (y)2=(x+y)2
-4+(y)2
=y2-4
=y2-22
=(y+2)(y-2)
(x+y)2=(y+2)(y-2)
(x+y)2=(y+2)(y-2)
(x+y)= ± (y+2)(y-2)
56"
Question 52. D. 8
You can apply the trial and error method here. Try replacing * with the given
numbers. Then, convert each resulting decimal to a fraction by dividing the decimal
digits by 100. Simplify the resulting fraction and determine which fraction will satisfy
the given condition for x.
Replace * with 2.
x = 0.22 = 22/100 = 11/50
Replace * with 3.
x = 0.23 = 23/100
Replace * with 7.
x = 0.27 = 27/100
Replace * with 8.
x = 0.28 = 28/100 = 7/25
Replace * with 9.
x = 0.29 = 29/100
As found, replacing * with 8 resulted to a one-integer numerator and a two-integer
denominator.
Question 53. B. – 5
Use the equation, 3a3 = 6b = 24 . Solve for a and b, respectively.
From the equation, we have:
3a3 = 24
a3 = 24/3 = 8
a=2
Also,
6b = 24
b=4
Plug these values into the expression, 2a 2 − 4b + 3 and simplify.
2
2a 2 − 4b + 3 = 2(2) – 4(4) + 3 = -5
©"SPECTRUM TUITION PTY LTD
57"
Question 54. B. 32
4
7
The numbers in the tick marks will form into an arithmetic sequence whose first term
is 12 and 8th term is 60. Express the 8th term using the first term 12 in order to find the
common difference. Use the formula: An = a1 + ( n − 1) d .
A8 = 12 + (8 − 1) d
60 = 12 + (8 − 1) d
60 = 12 + 7d
7d = 60 − 12
7d = 48
d = 48 / 7
Add this up repeatedly to 12 until reaching the 4th term, where d is located.
12, 18 6/7, 25 5/7, 32 4/7, 39 3/7, 46 2/7, 53 1/7, 60
Question 55. D. 28
Simplify this equation and solve for a.
( 2a − 3)( 2a + 3) = 7
4a2 – 9 = 7
4a2 = 7 + 9
4a2 = 16
a2 = 4
a=+2
Use either value of a and substitute it to the expression, 3a 2 − 5a + 6 .
3(2)2 – 5(2) + 6 = 12 – 10 + 6 = 8
3(-2)2 – 5(-2) + 6 = 12 + 10 + 6 = 28
©"SPECTRUM TUITION PTY LTD
58"
Question 56. E. d =
3x
The segment denoted by d is the diagonal of an inside right triangle whose two legs
are the height of the cube and the diagonal of the lower base of the cube.
The height of the cube is denoted by z but since x = y = z this can also be denoted by
x. The diagonal of the lower base of the cube has a length equal to 2 times the
length of each edge of the cube, say 2 x. Using Pythagoras’ theorem, we can solve
for d as follows:
d2 = x2 + ( 2 x)2
d2 = x2 + 2x2
d2 = 3x2
d=
3x
1,540, 000 p
12
Yearly Sales Tax = Yearly Sales × Tax rate
= 1,540,000 p
Question 57. D.
Average Monthly Tax = 1,540,000p /12
Question 58. C. 260
Vertical angles are congruent. Since ∠CAB and 820 angle are vertical,
then m ∠CAB =82.
The angles within a triangle add to 180o. Therefore, we can say that
m ∠CAB + m ∠B + m ∠C = 1800.
m ∠CAB + m ∠B + m ∠C = 1800
820 + 460 + 2a = 1800
1280 + 2a = 1800
2a = 1800 - 1280
2a = 520
a = 260
Question 59. D. 720
m ∠CAB + m ∠ADC + a = 1800
820 + m ∠ADC + 260 = 1800
1080 + m ∠ADC = 1800
m ∠ADC = 1800 - 1080
m ∠ADC = 720
©"SPECTRUM TUITION PTY LTD
59"
Question 60. A. 60 cm
In triangle ABD, AB = BD = AD = 10cm.
In triangle FEC, EC = FC = FE = 12cm.
In triangle GED, GE = ED = GD = 2cm.
DC = EC – ED = 12 – 2 = 10cm
FG = FE – GE = 12 – 2 = 10cm
AG = AD – GD = 10 – 2 = 8cm
Perimeter of ABCFG = BD + DC + CF + FG + GA + AB
= 10 + 10 + 12 + 10 + 8 + 10
= 60 cm
!
!
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
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60"
READING COMPREHENSION
EXAM PAPER 1
Detailed Solutions
Question 1: A
When reversing the sentence, the information about the surfer is given first. This
means that the information about the whale and its habitat must be given at the end.
The only option that does this is option A.
Question 2: C
The term sensation means a mental feeling, especially that of excitement. If the band
could produce this excitement, then the group would be said to be a hit. The other
choices are either antonyms (let down, failure, disappointment) or make no sense
(feeling).
Question 3: A
The child in the passage is nervous, excited, and in awe at the final sight of the horse.
When taking all of the feelings into account, A (anticipation) makes the most sense.
Though elation may also be true, the child is anticipating the excitement, not actually
overjoyed yet.
Question 4: B
Though anything is possible for the future of the passage, E is unlikely because the
horse is tied up; D is unlikely because of how forward the child is looking toward the
lesson; A would not be likely because of all the preparedness and excitement; C is
possible, but does not fit with the tone of the passage; and this leaves only option B.
Question 5: A
The narrator is omniscient since it seems to know and understand everything around
and uses terms like she said.
Question 6: E
Quotation marks tend to indicate dialogue in most passages, though some may
indicate quotes, this is still a form of dialogue, making E the only valid option.
Question 7: B
When an object is personified it is given human characteristics, in this case the blue
bell was speaking, which gives a flower a human ability.
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Question 8: D
Finn is both a proper noun and the beginning of the sentence which must be
capitalised. The list of actions require commas between each, and the correct ending
punctuation is a full stop. The only option to meet these criteria is option D.
Question 9: C
Tottered means to walk or move unsteadily on a surface. Cruising, crawling, leaping,
and dancing do not bring about the thoughts of unsteadiness. However, wobbled is an
unsteady gait such as tottered.
Question 10: A
The passage clearly states that Di was struggling with knitting ‘tried her patience over
a piece of knitting’.
Question 11: E
Parts of the passage mention what John would be doing if he were gentlemanly, but
he does not do those things. He is obviously not refined due to his actions, leading the
reader to believe he is the opposite of refined, which is uncouth.
Question 12: B
Based only on the final paragraph, Nan would be considered reminiscent because she
is reminded of and remembering times from the past.
Question 13: A
Judging by the final two lines, the line that would make the most sense would be one
about age.
Question 14: C
Though the poem begins with a reference to the worst day of their lives, this is said in
jest and elicits humour as if someone is making fun of getting older, but still being
very young.
Question 15: E
The crown that is referred to is on the child’s head and since it is clear nothing is there
except his hair, this is the logical answer.
Question 16: B
The child in the poem has died and gone to heaven to be with a ‘stronger father’. He
has gone to live in the clouds and sky.
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Question 17: D
The poem clearly states that he wants his father to toss him higher, all the way into
the sky, just as in option D.
Question 18: C
To make this sentence correct, Laura must be capitalized, a common should precede
the word but, and the appropriate punctuation, a full stop, must be added.
Question 19: C
The sentence has a very relaxed tone that makes it appear the llama is moving
casually, making option C the best choice. Ambling also means to move in a calm and
casual manner as does strolling.
Question 20: D
The reader must infer that the reason for removing the extra clothes was for safety as
the boys were about to try to swim ashore.
Question 21: A
The first sentence explains that the boys could not believe what had happened just a
few minutes earlier, meaning they were in shock.
Question 22: C
The passage clearly states that one boy was to go get a can of biscuits, option C.
Question 23: E
The boys were in such a hurry to get off the boat because of all the water, it appears
the phrase means the boat would possibly be underwater at any moment.
Question 24: D
A rolling stone gathers no moss means that one must move around, never get too
comfortable in a single position or everything could become routine and stagnant.
Question 25: B
Arthur had been practicing with his paints and after remembering his aunt had made
her own Valentines, he felt he could do the same. Arthur had not seen his aunt make
the cards, only remembered them so option B is the only one correct.
Question 26: C
The mother shows her confidence when she laughs at the child’s surprise at her
ability.
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Question 27: E
The story is very clear that Arthur received the paints for Christmas.
Question 28: E
•
•
•
Option I: This is correct, as radium was associated with another healthy
product (mineral water) as it was discovered in some mineral springs.
Option II: This is correct, as the US surgeon general endorsed radium as a
“cure for everything from malaria to diarrhea”.
Option III: This correct. Many believed that radium could improve health
(though this was not the case): it could cure insomnia and slow ageing, cure
malaria and diarrhea etc.
Question 29: C
•
•
•
•
Option A: This is incorrect, as there is nothing to suggest the motivation for
doctors supporting radium as a cure had to do with financial motivations
Option B: This is incorrect, as the article states people assumed radioactivity
was good for them as soon as it was found in the mineral springs, rather than
waiting for tests to confirm this.
Option C: This is correct, as “an entire industry was built on the supposedly
curative powers of radiation” before conclusive proof was given. This
suggests people were simply trying to profit off the new discovery, rather than
genuinely wanting to help people with illnesses and other health problems
Option D: This is incorrect, as there is nothing to suggest radium has any
health benefits
Question 30: C
This is a factual question: beauty cream, toothpaste and water are all mentioned in the
article as items containing radium.
Question 31: A
Paragraph 4 states that “There was no fancier way to be healthy in the 1920s than to
take a long soak in a radioactive bath at a radium spa”. The attitude to radium was
thus that it was a sophisticated and elegant product for sophisticated and elegant
people.
Question 32: B
The city is depicted as harsh, through phrases such as “smoke blows black
And the dark street winds and bends” and it is also oppressive, dampening the spirits
of the inhabitants (“We shall walk with a walk that is measured and slow”)
Question 33: D
Childhood is depicted as a carefree and natural time (“grass grows soft and white”),
free from the complications of the adult world.
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Question 34: B
The poem is a metaphor for growing up: the “sidewalk” represents the innocence and
beauty of childhood, and where the sidewalk “ends” is where adulthood (which is
harsh, unfair and oppressive) begins.
Question 35: D
The article hopes to convince people to start making their own crafts at home and then
selling them for profit. Option A is too broad, as the focus is on manufacturing, not
farmers in general. Option B is incorrect as no blame is being attributed for the
decline in home manufacturing: the situation is disappointing but the reasons behind it
are understandable to the author. Option C is incorrect as it is too broad: the author
does not want to create a general craft manufacturing industry, but rather an industry
in which domestic crafts are made for sale (option D).
Question 36: C
•
•
•
•
Option A: True, as the article states farmers would “chop up the bulky loom
for firewood”
Option B: True, as the article states “The profit of his easily acquired farm
land was so great and certain that it became almost a reproach to him to have
his womenkind busy themselves with other than necessary household duties”
Option C: Not true, as there is nothing in the article to suggest there was no
market for crafts; indeed, the passage suggests that travellers in particular
were interested in purchasing crafts.
Option D: True, as the article states that farmers “devoted the entire energy of
the family to the raising of crops.”
Question 37: D
The author refers to the “Indian curiosities” as “admirable and well-established” but
ultimately says “these hardly represent the mass of our people.” Thus, Option D is
correct: the goods were worthy, but did not represent American culture in an accurate
way.
Question 38: D
Option D is the only answer that has the required elements:
•
•
“Blankets knitted by women at home”: the author is concerned about domestic
crafts, rather than crafts made in factories or other places outside the home
“Sold at weekend markets”: the author is also concerned about ensuring that
these crafts are sold for profit, rather than simply given away or gifted.
Question 39: C
The proverb warns against doing something “in an instant” (that is, without thinking)
as doing so may require “an age to recompense” (in other words, it may take a long
time to fix the problems that occur as a result of such hasty actions.)
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Question 40: C
The clue is in the title: “No Vaccine, No School” as well as in sentence such as the
first (“Unvaccinated children should be held back from school and groups spreading
anti-vaccination messages should be punished”)
Question 41: D
Dr Hambleton’s frustration is revealed by comments such as “These vaccine objectors
''should be ashamed of themselves'' for spreading misinformation and should be
sanctioned” and “''We need to look at the groups providing those anti-vaccination
messages and we need to make sure we stop them . . . They are putting the
community in danger”. Option A is incorrect, because he does not accept the reasons
behind the parents’ decisions (in fact, he describes the reasons as “misinformation”).
Option B is incorrect because he is appalled at anti-vaccination groups rather than all
parents who refuse to vaccinate their children. Option C is incorrect because his tone
is passionate, rather than objective.
Question 42: C
Though the article may appear in a newspaper, the primary audience is intended to be
government legislators who have the power to deal with this issue.
Question 43: B
•
•
•
•
Option A is not true: The article suggests many parents have simply been
misinformed (though others do put “holidays” before their children’s
vaccination schedules)
Option B is true: Hambleton describes people’s beliefs about vaccination as
“misinformation”
Option C is not true: “''These are remote areas, regional areas and urban areas .
. . they are in high-income communities, low-income communities”
Option D is not true: Hambleton suggests that children be sent home during
outbreaks, but there is no evidence this is a current policy.
Question 44: C
Expert opinion is predominantly used, as quote from experts such as Hambleton and
Diane Watson are used to support the argument throughout the piece.
Question 45: C
The fable suggests that “It is too difficult to maintain a lie” – the monkey soon found
himself caught out by the dolphin because he was asked to support his original lie
with more details.
Question 46: D
The fact “the crew were obliged to swim for their lives” suggests this action was
necessary.
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Question 47: D
The Dolphin is cautious, as he asks many questions of the monkey rather than
accepting his story at face value. He is also vengeful, as he seeks to punish the
monkey for his lies.
Question 48: A
Option A is the only answer that:
• Spells “principal” correctly (“principal” refers to the person; “principle” refers
to a rule or regulation)
• Maintains a consistent tense: both “entered” and “became” are past tense verbs
• Has a comma only after room, to indicate a short pause between clauses
Question 49: A
Option A is the only answer that:
• Uses “except” to indicate an exception (rather than “accept” which means to
receive or agree to)
• Uses “lay” to refer to objects and “lie” to refer to people
Question 50: A
A psychiatrist aims to make a patient better, so “mitigate” most likely means to make
suffering “milder” (or less severe)
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
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NUMERICAL REASONING
TEST 2
Worked Solutions
Question 1: B – 1/3
In the pattern 4,6,24 the last number 24 is the product of the first two numbers 4 and
6. Accordingly, 3 is the product of 1/3 and 9.
Question 2: C – Each number in the series is a multiple of the first number in the
series.
In the pattern 3,27,36,6,12,21 all the numbers 27, 36,6,12,21 are multiples of 3
Question 3: A - $200
Since Alex will receive 40% of the profits and Marie will receive 50% of the profits,
in total they would be receiving 90% of the profit. The balance of 10% will be
donated to charity. Accordingly, the amount donated to charity will be 10% of $2000
i.e. $200.
Question 4: D – 100ml each from the two tumblers
Total amount of milk in the first two tumblers is 300ml + 300ml i.e. 600 ml. When
600 ml milk is divided equally into three tumblers, each tumbler will hold 600 ml
divided by 3 i.e. 200 ml each. To fill up the third tumbler with 200 ml of milk, 100 ml
will be taken from both the first two tumblers so that tumbler 1 will have (300 ml 100 ml), tumbler 2 will have (300 ml -100 ml) and tumbler 3 will have (100ml +100
ml i.e 200 ml)
Question 5: C - 12
If 4 people can dig a trench in 9 hours, then 1 person can dig it in 4 multiplied by 9
i.e. 36 hours. Therefore to dig the same trench in 3 hours, the number of people
required would be 36 divided by 3, i.e. 12.
Question 6: D - 32
The series consists of two alternate series 1,2,3,4,5,6 and 1,2,4,8,16. The missing
number comes from the second series where every number is double the previous
number. Hence the missing number is 16 x 2 = 32.
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Question 7: B - 9
Let the age of Penny in years be x. Then the age of Luke is 3x. In six years time
Penny’s age would be x+6 while that of Luke would be 3x + 6. Since in six years,
Luke would be twice as old as Penny, we can write 3x+6 = 2(x+6).
3x + 6 = 2(x + 6)
= 3x + 6 = 2x + 12
(Expand the brackets)
= 3x – 2x = 12 – 6
(Collect like terms)
=x=6
Solving for x we get x = 6.
Therefore, Penny is 6 years old now and will be 9 years old in three years time.
Question 8: A - 30
Let the first number be x.
The second number would be x+1
The third number would be x+2.
The sum of three consecutive numbers is therefore x+(x+1)+(x+2)=87.
Solve for x
x+(x+1)+(x+2) = 87
x + x + 1 + x + 2 = 87
(Expand the brackets)
3x + 3 = 87
3x = 87 – 3
3x = 84
(Divide both sides by 3)
x = 28
Substitute the x into the equation for the third number (x + 2)
Therefore the third number would be 28+2 = 30
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Question 9: C – 2 kilometres
Since both Bryan and his younger brother covered the same distance in the first half
an hour, they would be walking at the same speed. Since they covered 2 kilometres in
half an hour, their speed of walking is 4 kilometres per hour.
Therefore, in fifteen minutes they can walk 1 km each. However, since they walked in
different directions, the distance between them would be 1km + 1km i.e. 2 kilometres.
Question 10: D – 5 watermelons
12 mangoes weigh the same as 2 watermelons (6 x 2).
30 oranges weigh the same as 3 watermelons (3 x 10)
Therefore the two combined would weigh the same as 2 + 3 watermelons i.e. 5
watermelons
Question 11: B - 6
As there are two dog trainers, of the twenty eight legs, four belong to the trainers. The
rest of the twenty four legs belong to the dogs. 24 divided by 4 legs = 6.
Hence there are 6 dogs which are being trained.
Question 12: B - 1
Each number is double its previous number.
Question 13: C - 35
All other numbers are divisible by 3.
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Question 14: C – 9.00am
Trams from the depot are available at intervals of 5 minutes and the tram ride from
the depot to his office takes half an hour.
Trams leave from the depot 3 minutes fast so available times from 8:50am to 9:30am
are:
Departure 8.50am 8.55am 9:00am 9:05am 9:10am 9:15am 9:20am
times at
the depot
Actual
8:47am 8.52am 8.57am 9:02am 9:07am 9:12am 9:17am
time
Since it takes half an hour by tram to reach Mr. Moses’ office from the depot, he
needs to catch the tram before 9:00 AM real time.
The latest tram he can catch is the 8.57 am tram to arrive at the office by 9:30am.
According to his watch, this will be 9:07 am as his watch is 10 minutes fast.
If we work backwards from here,
9.07 am – 7 minutes (travel time to reach the depot from his house) = 9.00 am (latest
Mr. Moses can leave his home according to his watch.)
Question 15: B – 9.00 AM
Since Mr. Moses needs to catch the tram by 8:57 AM and the clock at the depot runs
fast by 3 minutes, the likely time displayed at the tram depot when Mr. Moses catches
the tram would be 9:00 AM.
Question 16: B - 12
The number in the third column of the first two rows are products of the numbers in
the first two columns in each row. Therefore the missing number would be 120
divided by 10, i.e. 12
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Question 17: A - 118
If the replacements are made, the grid would look like this
4
8
30
7
10
68
10
12
30 = 4 x 8 -2
68 = 7 x 10 -2
The missing number would be 10 x 12 – 2 = 118
Question 18: C – 13, 14, 182
The numbers in the first column follow the pattern, 4,7,10,13 where each number is 3
greater than the preceding number while the numbers in the second column follow the
pattern, 8,10,12, 14 where each number is two more than the preceding number.
Hence the grid would be
4
8
32
7
10
70
10
12
120
13
14
182
Question 19: C - 12
The pairs are such that the second number is the square of the first number.
Accordingly, 144 is the square of 12
Question 20: D - 29
We know that Oliver doesn’t have any more than 30 cars.
Using trial and error, we use the options presented to determine if any of the numbers
fit the clues given.
29 divided by 4 leaves a remainder of 1, divided by 3 leaves a remainder of 2 and
when divided by 5 leave a remainder of 4.
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Question 21: B - $5000
Every month Stephanie deposits an amount in the bank which is double the amount of
tax that she pays. Therefore, if she saves $10000 in the bank, she paid tax equivalent
to half that amount, i.e. $5000.
Question 22: D - 256
Starting from the third number in the series, each number is the product of the
preceding two numbers. The missing number therefore is 8 multiplied by 32 i.e. 256.
Question 23: C - 240
Let x = the number of gold coins in the jar be x.
2x = the number of silver coins.
If 20 gold coins are taken out and replaced by silver coins, the number of gold coins
left is x – 20. This is one third the number of silver coins which is 2x + 20.
Therefore 2x + 20 = 3(x – 20)
= 2x + 20 = 3x – 60
(Expand the brackets)
= -x = -80
(Collect like terms)
x = 80
(Divide each side by -1)
Solving for x we get x = 80.
To find the total number of coins in the jar
Gold coins = x = 80
Silver coins = 2x = 2(80) = 160
The total number of coins in the jar in the beginning was 80 + 160 = 240.
Question 24: C - 40
Since there were 240 coins in the jar, to have an equal number of gold and silver
coins, there should be 120 gold and silver coins each. Therefore 40 silver coins need
to be replaced by gold coins so that they are equal in number.
Question 25: D - 70
Steps
1. Draw a diagram, fill in all information,
and multiply price times quantity to get
the total value of each original lot and the
value of the total lot.
2. Set up the equation by adding $2800 to
the sum of the first and second lots. This
addition of $2800 equals the gain on the
entire transaction.
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Working
Let x = pairs in the second lot
50 pairs
x pairs
x + 50
$32
+ $40
= $60
32(50)
40x
60(x+50)
32(50) + 40x + 2800 = 60 (x + 50)
1600 + 40x + 2800 = 60x + 3000
-20x = -1400
x = 70
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Question 26: A – 30%
Number of participants in high jump = 50 – 18 – 17 = 15
Percentage of participants participating in high jump
=15/50 *100 = 30%
Question 27: B – 80%
Number of participants in high jump = 50 – 18 – 17 = 15
Number of students who did not receive awards: 15 – 3 = 12
Percentage of participants participating in high jump who did not receive awards:
=12/15 *100 = 80%
Question 28: A – Richard
The phrase "least variety of shoes" must be taken to mean different colours. Clearly
the answer is Richard, as he has black and white shoes only, while the others have
grey shoes as well. No arithmetic is needed for that.
Question 29: C– Daisy
Now, as we only know the relative value of the shoes, we can make things easier by
assuming that a pair of white shoes will cost $4, a pair of black shoes is worth
$1(black shoes fetch one quarter of the price of white ones at auction), and a pair of
grey shoes is worth $2(greys fetch half)
Anthony has (6 × $1) + (2 × $2) + (4 × $4) = $26 worth.
Richard has (16 × $1) + (2×$4) = $24 worth.
Daisy has (8 ×$1) + (6 × $2) + (2×$4) = $28 worth.
Mr. Shoeman has half what Richard has ($12 worth), plus two pairs of each ($14) for
a total of $26.
So the most valuable collection is Daisy's.
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Question 30: D - 23
Let a = greater number
Let b = lesser number
“The greater of 2 numbers is 7 more than the lesser”
a=b+7
“Three times the greater number is 5 more than 4 times the lesser number”
3a = 5 + 4b
Substitute a = b + 7 in the second equation:
3(b + 7) = 5 + 4b
3b + 21 = 5 + 4b
(Expand the brackets)
3b – 4b = 5 – 21
(Collect like terms)
-b = -16
(Divide each side by -1)
b = 16
b =16 so we plug it into the first equation to find a
a=b+7
a = 16 + 7
a = 23
Therefore:
a = 23 - the greater number.
Question 31: E – None of these
Let “a” be the first number and “b” the second number
a/b=5/1
a + b = 18
a / b = 5 / 1, a = 5b (cross multiply)
Substituting a = 5b into the equation: a + b = 18:
5b + b = 18
6b = 18
b=3
a = 5b = 5 × 3 = 15
Check: 15/3 = 5 and 3 + 15 = 18.
Question 32: C – 5.46pm
The race began at 4:15pm.
The first scooter finished at 5:30pm therefore, the second finished at 5:46pm.
Question 33: B – 7/8
Paul’s"Time"÷"Original"Record"Time:"
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Question 34: C – 20
To solve this problem, you have to know that half an hour is the same as 30 minutes.
Then you can divide 30 by 1 ½.
Step 1: Write the whole number and the mixed fraction as improper fractions:
!"
!
30 ÷ 1 ½ = ! ÷ !
Step 2: Write the reciprocal of the divisor, 2/3, and multiply:
!"
!
!"
!
30 ÷ 1 ½ = ! ÷ ! = = ! × !
Step 3: Simplify, if possible:
30 ÷ 1 ½ =
!"
!
!
÷!==
!"
!
!
× ! =20
Mighty Mart with this new system can get customers to self-checkout 20 customers
within 30 minutes.
Question 35: A
Let x represent the unknown quantity of flour Mary needs to make 25 kilograms of
the bread mixture.
The ratio statement is:
!"#$%&'!!"#$%
!"#$%&'!!"#$%!!"#!!"#(!.!.!"!!!)
so the proportion is:
!"!
!!
=
!"
!"#$
Solve for x by cross multiplying fractions:
!"
!
= !"
!"
20x = 25 × 12
20x = 300
x = 300/20
x = 15
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Question 36: D – 418 litres
You will have to find the area covered by the ceiling and walls (excluding the area
covered by the door and the window) separately.
Area of Ceiling = Length (L) × Breadth (B)
= 8m × 8m
= 64 m!
Area Covered by walls (4) = Length (L) × Breadth (B)
= 8 m × 6m × 4
= 192m!
Area covered by the door and the window = 6 m! + 14 m! = 20 m!
Therefore the area covered by walls excluding door and window
= 192m! - 20 m! = 172 !!
Water needed to wash:
Ceiling = Area covered by ceiling × water needed to wash a square metre of ceiling
= 64 m! × 2.5litres/m!
= 160litres
Walls (excluding area covered by the window and door)
= Area covered by walls (excluding area covered by window and door) × water
needed to wash a square metre of walls
= 172 m! × 1.5litres/m!
= 258 litres
Therefore John will need 418litres (258litres + 160litres) of water to wash the ceiling
and walls of his room leaving out the window and door.
Question 37: A - $10732.50
Fee per hour = $45
Number of hours = 6
Fee for the session = 6 * 45 = $270
Discounted Fee for the session = 270 * (100-5)%
= 270 * 95%
= $ 256.5
Students who qualified for discounted fee = 5
Students who were offered regular fee = 35
Total Fee Received = (5*256.5) +(35*270)
= $ 1282.5 + $ 9450
= $ 10732.5
Question 38: D - 50
Let x = the number of questions solved in day 1
x – 2 = the number of questions solved on day 2
x – 4 = the number of questions solved on day 3
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Form an equation:
x + (x-2) + (x-4) =150
x + x – 2 + x – 4 = 150
3x – 6 = 150
3x = 156
x = 156/3
x = 52
(Expand the brackets)
(Collect like terms)
(Divide each side by 3 to get x by itself)
Therefore, the number of questions solved on day 2 = x - 2 = 52-2 = 50 questions
Question 39: B - $14.66
Let x = the price of the pencil
2x = the price of the pen
The amount remaining after buying pen and pencil = 50 – x – 2x = 50 – 3x
The price paid for buying an eraser = (50-3x)/4
Amount spent on pen, pencil and eraser = $50-$10 = $40
Amount spent = x + 2x + ((50-3x)/4)
Thus, 40 = x + 2x + ((50-3x)/4)
40 = 3x + 50/ 4 + 3x/4
40 = 3x + 12.5 + 0.75x
3.75x = 27.5
x = 7.33
Price of pen = 2x
= 2* 7.33 = $14.66
Question 40: A - $7
Price of eraser = (50-3x)/4
Replacing the value of x in the equation
= (50-22)/4
= 28/4 = 7
Question 41: E – None of these
Let the list price of socks be x
Thus, 20% of x = $10
x = 10*100/20
x = $50
However, the sale price (SP) is the list price (LP) minus the trade discount (TD). As a
result:
LP – TD = SP
Thus, the sale price is $50-$10 = $40
Question 42: D – 114
Notebooks sold on Monday = 200 *30% = 60 notebooks
Notebooks for sale on Tuesday = 200 – 60 + 50 = 190 notebooks
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Notebooks sold on Tuesday = 190 * 40% = 76 notebooks
Notebooks remaining on Tuesday = 190-76 = 114 notebooks
Question 43: A - $8000
Sale amount of sandwiches = 1200 * 4 = $4800
Sale amount of hotdogs =400 * 8 = $3200
Total = $ 3200 + $ 4800 = $ 8000
Question 44: C $1600
Total Sales = $ 8000
Total Cost = (1200*3) + (400*7)
= 3600+2800
= $6400
Profits = Sales – Cost
= 8000-6400 = 1600
Question 45: C – 18 hours
Speed difference between the cars = 55 km – 50 km = 5 km.
Distance required = 90 km
Time required = 90 km / 5 km per hour = 18 hours
Question 46: A – 6 kilometres
Proportion of Distance covered at 4 km / hr = 2/3
Proportion of Distance covered at 5 km / hr = (1- 2/3) = 1/3
Time Spent = 1 hour 24 mins = 84 minutes
Thus, 84 = 14/3 D*3
Distance = 84 / 14 = 6 km.
Question 47: C – 32 days
5 women are equivalent to work done by 8 girls
Thus, 10 women can do equivalent of 16 girls
10 women and 5 girls are equivalent of 16 + 5 = 21 girls
If 8 girls can do the work in 84 days, then 21 girls can do a work in (8*84/21) = 32
days.
Question 48: B
Price quoted by showroom dealer = $ 50000
Add: Registration, Insurance & Other Expenses (12% of $50000) = $ 6000
On-Road Price of the Car ($ 50000 + $ 6000) = $ 56000
Loan Offered by the bank (in %age terms) = 60% of the on road price
Loan Offered by the bank (60% of $56000) = $33600
Deposit to be made by the purchaser = 56000-33600 = $22400
Question 49: C
Speed of the first train = 120/10 m/sec = 12 m/sec.
Speed of the second train = 120/15 m/sec = 8 m/sec.
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Relative speed = (12 + 8) = 20 m/sec.
Required time = (120 + 120)/20 sec = 12 sec.
Question 50: E – None of these
Annual Fixed Salary = $1500*12*12= $18000*12=$216000
Salary based on turnover = 950000 * 2% = $ 19000
Total Salary = $235000
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
©"SPECTRUM TUITION PTY LTD
80"
VERBAL REASONING
EXAM PAPER 2
Detailed Solutions
Question 1: B - Creak
Roar, thud and crackle are all onomatopoeic words, which means that they are words
that describe a sound. Creak is also an onomatopoeic word, as it can describe the
sound of a door opening.
Question 2: B - Seat
Sit, lounge and perch are all verbs that mean to sit. Seat, on the other hand, is a noun.
Question 3: C – My uncle
My mother’s father is my grandfather. His only daughter will be my mother. Her
brother will be my uncle.
Question 4: E – 3 and 5
If my middle name is my father’s first name (3) and my middle name is Glenn (5),
then my father’s name is Glenn.
You may be tempted to choose 2 and 4 or 1 and 2. But just because I live with a man
called Glenn (2) and I live with my father (4), doesn’t mean that Glenn is my father;
Glenn could be my brother. Also, just because my mother is married to a man named
Glenn (1) doesn’t mean that Glenn is my father; he could be my step father.
Question 5: B – The widths of circles
An anagram of DREAMIEST is DIAMETERS, which are the width of circles.
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Question 6: B – Some LERGs are LURGs.
The answer can be discovered through elimination and the use of a Venn diagram.
From here, we can clearly see that some LERGs are LURGs.
Question 7: C – 10 steps
Firstly, work out how many steps Christopher will take in each direction. He takes 11
steps forward (for each letter in Christopher), then turns left and takes 10 steps (2 for
each letter in Peter), then turns left again and takes 12 steps (3 for each letter in
Dean), then takes 1 step backwards. His path is shown below.
!
#
#
#
#
#
#
#
#
#
#
#
!
!
!
!
!
!
End
!
!
!
"
"
"
"
"
"
"
"
"
"
"
Start
#"
Christopher is 10 steps away from his starting position.
Question 8: B - lessen
Reduce, minimise and compress are all verbs that mean to make smaller. Lessen is
also a verb that means to make smaller.
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Question 9: C - blueyellow
GREEN
Must mean vampire, as it is in sentence 1 & 2
BLUE
Must mean scary, as it is the other word in sentence 1
YELLOW Must mean ghost, as in sentence 3.
or
PURPLE
So the word for scary ghost must contain the word blue and either purple or yellow.
Furthermore, as we can see from sentence 1, the word order remains the same when
the phrase is translated, so the word blue must come first. Therefore, the answer is
blueyellow.
Question 10: D – Painkiller is to headache
A cast is used to treat a fracture. A painkiller is used to treat a headache. Therefore
cast is to fracture as painkiller is to headache.
Question 11: C – No mammal is a goat
Put the information into a Venn-diagram.
A is true because friendly and goats overlap, so some friendly animals are goats.
B is true because fuzzy and mammals overlap, so some fuzzy animals are mammals.
D is true because friendly and goats overlap, so some friendly animals are goats.
C is false because all goats are mammals, therefore some mammals are goats.
Question 12: A – 2 and 5
If Lisa only enjoys salmon and tuna (statement 1), and Jenny hates salmon (statement
2), then the only fish that both Lisa and Jenny can like is tuna. If Lisa, Jenny and I all
share the same favourite type of fish (statement 4), then this fish must be tuna.
Therefore, I enjoy eating tuna. Statements 2 and 5 cannot be used to prove this
statement, so they are irrelevant.
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Question 13: C - Rachel
The answer can be found by making a table.
Bass
Drums
Piano
Ukulele
Craig
Lenny
Sally
Rachel
First, we learn that Craig doesn’t play a stringed instrument. Therefore, he can’t play
bass or ukulele.
Bass
Craig
Lenny
Sally
Rachel
Drums
Piano
✕
Ukulele
✕
Next, we learn that Sally is best friends with the ukulele player. Therefore, Sally
doesn’t play the ukulele.
Bass
Craig
Lenny
Sally
Rachel
Drums
Piano
✕
Ukulele
✕
✕
Finally, we learn that Lenny’s instrument has keys. Therefore, Lenny plays the piano.
Bass
Craig
Lenny
Sally
Rachel
✕
✕
Drums
✕
Piano
Ukulele
✓
✕
✕
✕
Now we know that neither Craig, Lenny or Sally play the ukulele. Therefore, Rachel
must play the ukulele.
Bass
Craig
Lenny
Sally
Rachel
✕
✕
Drums
✕
Piano
✓
Ukulele
✕
✕
✕
✓
Question 14: B - Herb
The anagram of PLAYERS is PARSLEY. This is the name of a herb.
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Question 15: C - Sketch
Print, type and jot are all verbs that describe writing something down. Sketch means
to draw, so it is the odd one out.
Question 16: C - Touchy
Irritable is an adjective that means easily annoyed or upset. Touchy is also an
adjective that means easily annoyed or upset.
Question 17:B - Miguel
Firstly, find out the order after the first lap. Billy was ahead of Ian but behind Sia.
Sia
Billy
Ian
Miguel was ahead of Billy but behind Sia.
Sia
Miguel
Billy
Ian
Then, work out how the order changed during the second lap. Ian overtook everyone
to come first.
Ian
Sia
Miguel
Billy
Then Miguel was overtaken by another runner, who must have been Billy.
Ian
Sia
Billy
Miguel
Therefore, Miguel came last in the race.
Question 18: E - Hatred
Adoration means love. The opposite of love is hatred.
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Question 19: A - Cheerful
Cantankerous means bad tempered or irritable. The opposite of this cheerful.
Question 20: B – Relaxed is to tense
Practical is the opposite of frivolous. Relaxed is the opposite of tense. Therefore,
practical is to frivolous as relaxed is to tense.
Question 21: B – Some JOOBs are HOOBs
The answer to the question can be found through elimination and the drawing of a
Venn- diagram. Note that we don’t know the relationship between ZOOBS, TOOBS
and the other categories.
A is false because only some LOOBs are JOOBs.
C is false because we don’t know for sure whether any ZOOBs are JOOBs.
D is false because only some TOOBs are ZOOBs.
B is true because some JOOBs are clearly HOOBs.
©"SPECTRUM TUITION PTY LTD
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Question 22: C - Don
The answer can be found through a table:
Software engineer
Optometrist
Wall St Broker
•
•
•
•
Patricia
X
YES
X
Susan
X
X
YES
Don
YES
X
X
We know that Don was not at the picnic, therefore he is not the Wall Street
broker.
We know that Patricia is neither the software engineer, nor the Wall Street
broker (as she cannot join herself for a picnic). Therefore, through
elimination, she must be the optometrist.
Since neither Patricia nor Don are the Wall Street Broker, Susan must be.
Since Patricia is the optometrist and Susan is the Wall Street broker, Don must
be the software engineer.
Question 23: A - 1
The answer can be found by listing the people in the order they stand. We know that
Marty is flanked by Jack and Ned.
Jack
Marty
Ned
We also know that there are two people between Beth and Jack. These two people
will be Marty and Ned.
Jack
Marty
Ned
Beth
We also know that I stand next to Beth.
Jack
Marty
Ned
Beth
Me
From here, we can see that there is only one person between myself and Ned.
Question 24: B - Expose
Protect is a verb that means to shield something or someone from danger. Expose is
the opposite of this.
Question 25: A - Preserve
Displace, relocate, shift, move, shuffle and disturb are all verbs that mean to move
something. On the other hand, preserve means to keep something the same.
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Question 26: C - Jemma
As you read each piece of information, write the runner’s names in the correct order.
With half a mile to go, Jemma was ahead of Kim.
Jemma
Kim
Laura was ahead of Jemma.
Laura
Jemma
Kim
Elena was directly behind Laura.
Laura
Elena
Jemma
Kim
At the finish line, Kim overtook the person in front of her.
Laura
Elena
Kim
Jemma
Elena then fell over and came last.
Laura
Kim
Jemma
Elena
As we can see, Jemma came third.
Question 27: A – smaller, cat, bigger
ZZ and
SEEP
CLOBBO
BREEP
WOOFO
GEEKO
Are the repeated words in each sentence, so they must mean is and than
Is repeated in the first sentence, so it must mean dog
Is repeated in the first sentence, so it must mean cat
Is only in the first sentence, so it could either mean my, smaller or
everyone’s
Is only in the second sentence, so it could either mean your, bigger or
nobody’s
Based on this information, the only possible answer is A.
©"SPECTRUM TUITION PTY LTD
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Question 28: D – Flattered is to compliment
To make something random, you shuffle it. To make someone flattered, you
compliment them. Therefore, random is to shuffle as flattered is to compliment.
Question 29: C – Lisa and Maria
As you read each piece of information, add the girls’ names to a list. Jenny is latter
than Fiona, but shorter than Lisa.
Lisa
Jenny
Fiona
Claudia is only taller than Maria. Therefore, Claudia and Maria are the two shortest.
Lisa
Jenny
Fiona
Claudia
Maria
The first and last people in line will be Lisa and Maria.
Question 30: D – Some GIPs are GUPs
This can be demonstrated using a Venn diagram.
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A is false because only some GUPs are GOPs. B is false because some GEPs are
GIPs. C is false because some GEPs are GUPs. D is true because some GIPs are
GUPs.
Question 31: C - Trick
Hustle, scam and swindle are all verbs to describe fooling someone into something.
Trick is also a verb for fooling someone.
Question 32: A – 1 and 4
If there are 3 men in my family, Tony, Ted and Ted (statement 1) and my older
brother is named after my father (statement 4), then my older brother and my father
must both be the two Teds in the family. Therefore, my brother’s name is Ted. No
other statements can be used to prove this conclusion.
Question 33: B – Pyramid is to triangle
A cube is a 3-dimensional equivalent of a square. A pyramid is a 3-dimensional
equivalent of a triangle. Therefore, cube is to square as pyramid is to triangle.
Question 34: C - Forger
Kidnapper, arsonist and thief are all nouns to describe people who have committed
specific crimes, such as kidnapping, arson and theft. Forger is a noun to describe
someone who has committed the crime of forgery.
Question 35: A - Moral
Fiendish is an adjective that means excessively cruel or evil. The opposite of this is
moral, which means ethical and good.
Question 36: D - beverage
I start with the letters CRIED and switch the last two letters to get CRIDE. Then I
take the second letter (R) and put it at the end of the word to get CIDER. This is the
name of a beverage.
Question 37: A - Bring
Raise, nurture and rear are all verbs that mean to look after a young person or animal
as it grows. Bring does not fit with this meaning.
Question 38: B – 2 and 3
If someone’s hat is on fire (statement 1) and only one thing is on fire (statement 4),
then the one thing that is on fire must be a hat. If one of Jessica’s items of clothing is
on fire (statement 5), then it must be her hat, since a hat is the only thing that is on
fire. Therefore, Jessica’s hat is on fire. Statements 2 and 3 can not be used to prove
this statement.
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Question 39: C - Gary
After Tony switches Gary and Jeremy’s drink, Jeremy has the poison.
After Gary switches Jeremy and Tony’s drink, Tony has the poison.
After Gary switches his and Tony’s drink, Gary as the poison.
Question 40: A - Unruffled
Desperate is an adjective that means full of urgency. Unruffled is an adjective that
means uncaring or unphased, which is the opposite of desperate.
Question 41: C – Gargantuan is to minute.
Braggadocios is the opposite of humble. Gargantuan is the opposite of minute.
Therefore, braggadocios is to humble as gargantuan is to minute.
Question 42: C – GEEP MEEP HORN
MEEP and GEEP appear in the first and third sentences, so they must mean you and
are. None of the phrases contain the word what, so what can’t be SEEP, LOOP, MIX,
NIX, MEEP or GEEP. The only answer that fits with this information is C.
Question 43:D - Negligent
Watchful is an adjective to describe someone who is paying lots of attention.
Negligent is an adjective to describe someone who is not paying enough attention or
care to something.
Question 44: A - Bemoan
Bemoan is a verb that means complain.
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Question 45: A - Amy
Draw a circle and add names as you get more information. Firstly, we learn that
Bessie is between Gus and Daisy. However, we don’t yet know who is on the right of
Bessie and who is on the left.
Next we learn that Hector is third to Bessie’s left.
We also learn that Hector is second to Amy’s right.
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Already, we can tell that either Amy or Hector will be sitting opposite to Daisy. The
last piece of information we get is that Carl is sitting between Amy and Gus. This
helps us to figure out that Gus must be to Bessie’s right and Daisy must be to Bessie’s
left.
We don’t need to fill out any more of the diagram, because we can now see that Amy
is sitting opposite to Daisy.
Question 46: D – 2 and 4
If Jeremy doesn’t have enough money to buy a burger but can buy a sausage role,
then he must have between $3.50 and $5.00 (statement 2). If Jeremy only has gold
coins in his pocket (statement 4), then the amount of money he has must be in exact
dollars. The only exact dollar amount between $3.50 and $5.00 is four dollars.
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Therefore, by combining these two statements, we prove that Jeremy has four dollars
in his pocket.
Question 47: C – No KIGGLES are YIGGLES
This can be demonstrated using a Venn diagram.
A is true because there is an overlap between WIGGLES are YIGGLES.
B is true because there is an overlap between KIGGLES and JIGGLES.
D is true because there is an overlap between KIGGLES and YIGGLES.
C is false because there is an overlap between KIGGLES and YIGGLES.
Question 48: B – Cheap
Meagre, economical and stingy are all adjectives that mean cheap. So cheap would
also fit on the list.
Question 49: C – Jealousy is to rival
Romance is a feeling that a wife might make you feel. Jealousy is a feeling that a rival
might make you feel. Therefore, romance is to wife as jealousy is to rival.
Question 50: B – Duster is to rusted
Singer is an anagram of resign. Duster is an anagram of rusted. Therefore, singer is to
resign as duster is to rusted.
Question 51: B - Drum
Pop, rock, jazz, punk, metal and techno are all genres of music. Drum is an
instrument, not a musical genre.
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Question 52: C - Tranquility
Bedlam means chaos. The opposite of this is tranquility, which means peace.
Question 53: B - 2
I was born when Claire was learning to talk (statement 4), which happened when she
was 3 (statement 5). Therefore, Claire is 3 years older than me. If I have another sister
called Jacqui (statement 1) and Claire is 5 years older than Jacqui (statement 2), then I
am 2 years older than Jacqui. Therefore, I am the middle child. Statement 2 is
irrelevant to this proof.
Question 54: A - mootgeek
The English translations for this language are as follow:
MOOT or
GORM
CORK
BEEP
ZEER
Either one of these words must mean golden.
Must mean medal, as in the second and third sentences.
Must mean silver, as in the second sentence.
Must mean winner, as in the third sentence.
The word for golden coins must contain either MOOT or GORM, and can’t contain
CORK, BEEP or ZEER. Mootgeek is the only answer that fits this information.
Question 55: B – 2 & 4
If I had $20 before winning a competition (statement 2), and I had $120 after the
competition (statement 4), then I must have won $100 in the competition.
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Question 56: E – Cannot tell
As you read each piece of information, add the archers’ names to a list. Firstly, Janet
scored more than Georgia but less than Ace.
Ace
Janet
Georgia
Louise scored more than Janet but less than Ace.
Ace
Louise
Janet
Georgia
Suzie scored less than Janet. However, we don’t know if she scored more or less than
Georgia.
Ace
Louise
Janet
Georgia/Suzie
We don’t know whether Georgia or Suzie cam last.
Question 57: D - Paprika
As you read each piece of information, add the spices to a list. There is twice as much
parsley as coriander and three times as much cumin as coriander.
Cumin
Parsley
Coriander
There is more paprika than parsley, but less than there is cumin.
Cumin
Paprika
Parsley
Coriander
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The third most common ingredient is salt and the second most common ingredient is
pepper.
Cumin
Salt
Pepper
Paprika
Parsley
Coriander
Paprika is the fourth most common ingredient.
Question 58: D - Take
Component, piece and ingredient are all words that mean a smaller part of something
larger. Take is the odd word out.
Question 59: A – Destroy is to damage
Love is a more intense version of like. Destroy is a more intense version of damage.
Therefore, love is to like as destroy is to damage.
Question 60: B - Mark
Remove, delete and eradicate are all verbs that mean to get rid of something. Mark is
the odd word out.
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
©"SPECTRUM TUITION PTY LTD
97"
MATHEMATICAL REASONING
EXAM PAPER 2
Worked Solutions
Question 1: A - 10
Steps
Rules:
+ and + = +
- and - = +
- and + = + and - = 1. Convert any double signs to a
single sign. For example + – can be
replaced with a – sign and – – can be
replaced with a + sign.
Working
–12 + –6 – – 5 + 3 =
–12 – 6 + 5 + 3 =
2. Simplify the operation
–12 – 6 + 5 + 3 =
–18 + 8 = –10
Question 2: C - 7
Steps
1. First divide –105 by –3. When
dividing a negative number by
another negative number, it becomes
a positive number.
Working
–105 ÷ –3 =!35
2. Divide 35 by 5 to find the answer.
35 ÷ 5 = 7
Question 3: D
Steps
1. To find out how much deposit he
paid we multiply the cost of the boat
by 20%.
Working
$4000 x 20% = amount of deposit
2. Convert the percentage to a
decimal
3. Multiply $4000 by 0.20
4. Work out the remainder he has to
pay by subtracting the amount of
deposit from $4000.
20/100 = 0.20
©"SPECTRUM TUITION PTY LTD
$800
$4000 – $800 = $3200
98"
Question 4: C - -46
Steps
1. Using BODMAS (Brackets,
Orders, Division, Multiplication,
Addition, Subtraction), we prioritise
the operation inside the bracket first.
Working
15×−2 − (18 − 10) + 64 ÷ −8 =
15×−2 − 8 + 64 ÷ −8 =
2. The next operation is division or
multiplication going from left to
right. Just pay attention to the sign
change. Multiplication or division
between two numbers with equal
signs will always produce a positive
number. If the two numbers have
different signs, then it will always
produce a negative number.
15×−2 − 8 + 64 ÷ −8 =
−30 − 8 + −8 =
3. Convert any double signs to a
single sign and then perform the final
operation.
−30 − 8 − 8 = − 46
Question 5: C
Steps
1. 18% of $8000 can be calculated by
converting the percentage to a
fraction and multiplying by $8000
Working
18 8000
×
100
1
2. Cancel out the zeroes
18 80
×
1
1
3. Multiply across
18×80 = $1440
Alternative solution
You could also convert the percentage to a decimal, which is equivalent to 0.18 then
multiply by $8000 = $1440
©"SPECTRUM TUITION PTY LTD
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Question 6: E – 4.2m
Steps
1. Convert all the measurements into
metres using the conversion chart
below:
Working
A. 520 cm ÷ 100 = 5.2 m
B. 5.6 m = 5.6 m
C. 4600 mm ÷ 1000 = 4.6 m
D. 0.0062 km x 1000 = 6.2 m
2. Find the shortest distance
E. 4.2 m = 4.2 m
4.2 m
Question 7: B – 88m
Steps
1. Fill in all the missing lengths in the
diagram
2. The perimeter is calculated by
adding the length of all sides of a
shape. Count the number of sides
with the same length.
3. To find the total perimeter, we
multiply the number of sides by its
respective length and add them all
together.
Working
There are 8 sides with the length of 4 m.
There are 2 sides with the length of 8 m
(16 – 8m).
There are 2 sides with the length of 20m
(28 - 8m).
(8×4) + (2×8) + (2×20) =
32 + 16 + 40 = 88 m
Question 8: B – 8 cm
Steps
1. The ratio of the length of arc and
the angle of arc is same as the ratio of
the circumference of the circle and
the angle of one revolution (=360˚).
Using this knowledge we can write.
Working
Ratio of the length of arc and the angle of arc
= 11 cm / 45˚.
Ratio of the circumference of the circle and
the angle of one revolution
= C (circumference of the circle) cm / 360˚
11 cm / 45˚ = C cm / 360˚
2. Solve the equation for C by
multiplying 360˚ to each side.
C = 11 cm x 360˚/45˚ = 11 cm x 8 = 88 cm
©"SPECTRUM TUITION PTY LTD
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Question 9: C - 180
Steps
Working
1. Identify the ratio between spigs 3 spigs : 1 spog,
and spogs and between spogs and 5 spogs : 1 spug.
spugs
2. Use these ratios to calculate how To make 1 spug, we use 5 spogs.
many spigs in 12 spugs.
Therefore in 12 spugs we would have used :
12×5 = 60!!"#$!
To make 1 spog, we use 3 spigs.
Therefore in 60 spogs we would have used:
60×3 = 180 spigs.
So, we will use 180 spigs to make 12 spugs.
Question 10: B - 27
Steps
Working
2 2
1. Let the value of the unknown
3 : 5 = 17: !
number be x
5 5
2. Convert mixed
improper fractions.
numbers
to 17 27
:
= 17: !
5 5
17 27 17
3. Re-express ratios as fractions.
For example a ratio of 1:6 can be 5 ÷ 5 = !
represented as 1/6.
4. Simplify the left hand side.
17 5
17
×
=
5 27
!
17 17
=
27
!
17
5. Solve for x by rearranging the
!=
×!27 = 27
equation.
17
©"SPECTRUM TUITION PTY LTD
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Question 11: C - 65 tonnes
Steps
Working
1. If we add 7 tonnes of screening, 2 7 + 2 + 13 = 22 tonnes.
tonnes of cement, and 13 tonnes of
sand altogether, we will have 22
tonnes of concrete.
2. Since we need to make 110 tonnes
of concrete, we need to have 5 times
that of each ingredient.
!!"
!!
= 5,
5 x 7 = 35 tonnes of screening,
5 x 2 = 10 tonnes of cement, and
5 x 13 = 65 tonnes of sand
3. The amount of sand required to 65 tonnes.
make 110 tonnes of concrete is:
Question 12: B - 45°
The fundamental property of triangles state that the sum of all the internal angles is
equal to 180°. Straight lines = 180°.
Steps
Working
1. Calculate the measurement of the 180° – 130° = 50°
internal angle from the external angle.
2. Now that we have two internal 180° = α + 85° + 50°
angles, calculate the third angle.
α = 180° −!135°
α = 45°
Question 13: C - 53°
Steps
Working
1. Since opposite diagonal angles of a
parallelogram are the same, we can
see that the angle adjacent to our
external angle is the same as that
initially provided to us.
2. Now using the adjacent angle External angle = 180°−127° = 53°
principle we can find the unknown
angle by subtracting the internal
angle from 180°.
©"SPECTRUM TUITION PTY LTD
102"
Question 14: B – 14
From the graph it can be observed that the number of students studying more than 7
hours i.e., studying 8, 9 and 10 hours is 5 + 4 + 5 = 14
Question 15: A – 29
From the graph it can be observed that the number of students studying for 5 hours or
less i.e., 5, 4, 3, 2 and 1 hours are 9 + 7 + 5 + 2 + 6 = 29"
!
Question 16: A – !"
Steps
1. Probability of an event is
calculated by using following
equation.
2. Work out the number of desired
outcomes.
Working
Probability =
Number!of!desired!outcomes
Number!of!all!possible!outcomes
The outcomes of an event where the sum of
both dice is 8 are: (2,6), (3,5), (4,4), (5,3),
and (6,2). Therefore, there are 5 outcomes the
sum can be 8.
3. Work out the number of all There are 6 outcomes of rolling a dice: (1)
possible outcomes.
,(2) ,(3) ,(4), (5), (6). Since two dices are
rolled at the same time, we multiply the
number of outcomes of rolling each dice
together.
6×6 = 36 outcomes
4. Work out the probability.
5
36
!
Question 17: B – (− !)
The formula for finding the gradient from the given sets of coordinates is
!!!!!
Gradient = !!!!!
!! !!
!
Gradient = !!!! = − !
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103"
Question 18: B – (3,0)
The line cuts the x-axis on the positive side therefore the set of coordinates satisfying
this question should have a positive x coordinate, therefore the answer is option B
(3,0)
Question 19: A – (– 10 < x ≤ 9)
According to the statement this is the only inequality that satisfies it as “x” is greater
than -10 and equal to and less than 9 in it.
Question 20: B. – (−17−15x)
– 5 3x + 6 + 13
(Expand the brackets)
= ! −15x − 30 + 13
(Combine like terms)
= ! −15! − 17
(Sometimes the answer is rearranged)
Question 21: E – None of these
The figure is called a trapezoidal prism and a possible answer is below
©"SPECTRUM TUITION PTY LTD
104"
Question 22: B – (!" + !" !" m)
John runs two times straight along the shorter sides and two times along the diagonal.
Steps
1. Find the distance John runs along the
shorter sides (A to B and from D to C)
2. Find the distance of the diagonal by
using Pythagoras’ theorem
(!! + ! ! = ! ! )
Working
20×2 = 40!!
Diagonal
= 50! + 20! = ! !
2900! = 29!×100
=10 29
Total distance along diagonals =
10 29!×2 = 20 29!!!
3. Add the distances together
40 + 20 29!!
Question 23: A - 15 !
Steps
1. Write the equation
Working
5! 63 = ?
2. Does 63 contain any factors?
3. Are any of the factors perfect squares?
4. Rewrite
Yes: 7 and 9
Yes: 32 = 9
5. Find the square root of the perfect
square and move it out
6. Multiply 5 and 3 together
7. Find the answer
©"SPECTRUM TUITION PTY LTD
63 ! = !! 3! ×7!!
= !!3! 7
5×3!! = !!15:"
!ℎ!"!#$"!!!5×3! 7"
!"#$%&:!15! 7"
105"
Question 24: B – 5cm
Steps
1. Find the length of the base for the
triangle. For the length of the base we can
find it by subtracting the top horizontal
side of the rectangle from the total length
of the bottom side.
2. We can calculate x by using
Pythagoras’ theorem (!! + ! ! = ! ! )
The length of the perpendicular is the
same as that of the vertical side of the
rectangle i.e. 4cm
Working
Length of base = 8−5 = 3!!"
Using Pythagoras’ theorem
! = ! 4! + 3!
! = 16 + 9
! = 25
x = 5cm
Question 25: C - !!!"
Steps
Working
1. To find the distance AG we first find
the distance diagonally between E and G
and then using it we find the distance
between A and G.
!" =
First we apply Pythagoras’ theorem to
find the distance EG
2. Using EG we again apply Pythagoras
theorem to find AG
=
!"! + !" !
3! + 4!
= 9 + 16 = 5!!"
!! =
!" ! + !" ! =
5! + 1! = 6!!"
Question 26:"A - $2600
!
The car was purchased for $6500 and was reduced by !
!
!
First calculating ! of $6500 = ! ×!
!"##
!
Cancel out the 5 by dividing into 6500
3 5×1300
!×!
5
1
3!×!1300 =!$3900
So the new price of the car will be calculated by subtracting this value from the
original price.
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106"
New Price = Old Price - $3900 = $6500- $3900 = $2600
Question 27: E - None of these
As provided Density = Mass / Volume
We have density = 3.9 g/cm3 and dimensions of the box. To calculate mass we need
volume which can be calculated from the dimensions of the box.
Volume = length ×breadth!×height = 2×4×8 = 64!cm!
Now calculating Mass
Mass = Density ×Volume = 3.9×64 = 249.6!
Hence the answer is none of these.
Question 28: C - 66.67 m/s
The information provided indicates that the car covers 60 km in 15 minutes.
Firstly we calculate speed in km/h. For that we will calculate the distance covered in
one hour.
15 minutes is a quarter of an hour so to find the distance covered in one hour we
multiply distance covered in 15 minutes by 4.
Distance covered in 1 hour = distance covered in 15 minutes ×4 = 60×4×240!"
So the speed of the car in km/h is 240km/h
Converting it into m/s
!"#
240 km/h = !"## ×1000 = 66.67!!/!
Question 29: C - − ! ∗ ! − ! − !
R =!
!!! !!
!
!×! = ! − ! + 3
Multiplying both sides with P
!×! − 3 = ! − !
Subtracting 3 from both sides
−! = !×! − 3 − !
Subtracting S from both sides
! = −( !×! − 3 − !)
Multiplying −1!!"!!"#ℎ!!"#$!
Note: the * is used in place of the multiplication sign. Occasionally the answer
will not look exactly as your final answer so you need to decide whether the
option is presented differently.
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Question 30: A – x > -13
Steps
Working
1. Write out the equation
2. Subtract 1 from both sides
3 7−!
5
=
3 7−!
5
+ 1 < 13
< 12
3. Multiply both sides by 5
= 3 7 − ! < 60
4. Expand the bracket
= 21 − 3! < 60
5. Subtract 21 from both sides
= −3! < 39
6. Divide each side by -3
= ! > −13
As x is a positive and -13 is a negative, x
will be greater than -13
!
Question 31: A - ! !" Steps
Working
1. Write out the equation
2. Multiply both sides by the lowest
multiple of 7 and 3 (=21) to get rid of
fractions.
21×
1
1
2! − 3 − 21× 3! − 7
7
3
= 21×−2
3 2x − 3 − 7 3! − 7 = ! −42
3. Expand the bracket on the left hand
side.
3 2x − 3 − 7 3! − 7 = ! −42
3×2x − 3×3 − 7×3x − 7×−7 = −42
6! − 9 − 21! + 49 = −42
4. Collect the like terms on the left hand
side.
6! − 21! + 49 − 9 = −42
5. Subtract 40 from both sides.
−15! + 40 − 40 = ! −42 − 40
−15! + 40 = ! −42
−15! = −82
6. Divide both sides by -15 to solve for x.
Since all options are in proper fractions,
©"SPECTRUM TUITION PTY LTD
−15!
−82
=−
−15
−15
108"
covert the answer to proper fraction.
! =!
82
7
=5
15
15
Question 32: A – y = 3x-2
To prove this is the equation of the line put 0 in place of x and y separately to find the
intercepts.
Putting ! = 0! => !! = 3(0) − 2! => !! = −2 hence intercept (0, −2)
!
Putting ! = 0! => !0 = 3! − 2! => !! = ! ! = 0.667 hence the intercept (0.667,0)
If we try for the other options then one or both of their intercepts will be wrongly
placed on the coordinate map. Hence this is the only equation which satisfies this line.
Question 33: B - (6,9)
The graph represents that only the set (6,9) can lie outside the region.
!"
Question 34: C – ! = ! − ! + !
To verify this is the correct option, place values of both intercepts separately to
confirm.
Putting (0,3) => ! = ! −
! !
Putting (2,0) => ! = ! −
! !
!
!
+ ! => 3 = 0 + 3 => 1 = 1
+ ! => 0 = −3 + 3 => 0 = 0
Hence this is the correct equation to satisfy this line
Question 35: A - (2,3)
The set (2, 3) is the only option as the lines intersect in the 1st quadrant where both x
and y are positive.
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Question 36:"B - 64
Steps
Working
1. Write out the problem.
−(−4)!
2. Expand the bracket.
!! = !×!×!
−4! = ! −4×−4×−4 = −64
3. Multiply -64 by -1 to answer the
question.
Question 37: A -
−1×−64 = 64
!!! !
Steps
Working
1. Write out the problem.
5! ! 6! !
×
6!
!
2. Cancel out any common factors
between numerators and denominators
using the index rule. In this case, y and x
can be cancelled out using the rule.
!!
= !!!! = !!
!!
3. Simplify the numeral part to answer
the question.
30! ! !
= 5x ! y!
6
Question 38: D -
5×6! ! ! ! 30! !!! ! !!!!! 30! ! !
=
=
6!"
6
6
!"#!
3! ! ! ∗ 2!" !
= 1 ! ! ∗ 2! 1
Any constant or variable with index 0 becomes equal to 1
= 2!! !
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Question 39: B - !! /!!!
Steps
Working
3! !! ! !
6! ! ! !!
1. Write out the problem.
2. Simplify the powers using index rule.
!!
= !!!! = !!
!!
!!! ×!! = !!!!! = !!! =
1
!
3! !! ! !
3! !!!! ! !!!!
=
6! ! ! !!
6
3! !! ! !!! 3! !! ! !
=
=
6
6
3. Simplify the numeral part and turn the
equation into positive power to answer
the question.
3! !! ! !
y!
= !!
6
2x
!
Question 40: D – (!"! )!
Steps
1. Write out the problem.
2. Try to change each option similar to
the problem.
Working
!
32!
Option"A:"Use" !!
!
!
!
= !!×! = !!" "
!
(32! )! = 32!×! = 32! !!"
!
!
Option"B:"Use" !! = ! ! !"
!
!
32! = 32! !"
Option"C:"Use" !!
!
!
!
= !!×! = !!" "
!
(32! )! = 32!×! = 32! !!"
Option"D:"Use" !!
!
!
!
= !!×! = !!" "
!
(32! )! = 32!×! = 32! !!"
!
Option"D"is"not"the"same"as"32! "
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Question 41: A – 16
According to the Venn diagram, the total number of students is = 5+6+3+2=16
Question 42: B – 2
According to the Venn diagram, the number of students not playing the instruments
=2
Question 43: B – 8
According to the Venn diagram the number of students playing only one instrument is
= 5+3 = 8
Question 44: C – 6
According to the Venn diagram the number of students playing both instruments is 6
Question 45: C - $240
John gets $12 back on every $10 that he invests.
Meaning he gets a profit of $2 for every $10 that he invests.
First we calculate the profit that he earns on every $1 that he invests = 2/10 = $0.2
Multiplying it by $200 we get the profit on this amount to = 0.2*200 = $40
Hence the total amount he gets back: = $40 + $200 = $240
Question 46: A – !! − ! !"
Steps
Working
1. Write out the equation.
2 5− 2
2. Expand the bracket using
multiplication theorem.
!−!
!
= !! − 2!" + ! ! "
2 5− 2
= 2!
5
!
!
!
= 2 5
!
− 4 5×2 +
− 2×2 5× 2! +
!
2 "
!
2 "
= 4×5 − 4 10 + 2"
= 20 + 2 − 4 10"
3. Collect the like terms to
answer the question.
©"SPECTRUM TUITION PTY LTD
= 22 − 4 10!
112"
Question 47: A -
!
!
!
We have to evaluate ! − !
Putting in values of x, y and z =>
!
!
!
!
!
!
−!=2−!=
!!!
!
!
= !!
Question 48: C - !"!! − !!!
!4!! − 2! !4!! + 2! "
= !4! 4! + 2! − 2! 4! + 2!
Multiply the first polynomial with the second.
= 16!! + 8!" − 8!" − 4! !
Simplify the polynomial expression
= 16!! − 4! !
Question 49: C – ! ! − ! ! + !
Steps
Working
1. Write out the equation.
4!! + !4! − !24
2. Take out 4 from each term as it is the
highest common factor.
= 4 !! + ! − 6
3. Factorise the terms inside the bracket
using the cross method.
!! + ! − 6
2
2
Write down factors of a below a
"
!!!!!!!!!!!!! + 3
!!!!!!!!!!!!! − 2!
Write down factors of -6 below -6
3a -2a = a
When multiplied, each factor as
indicated in the diagram and the sum of
two products give the value of the
second term. The equation can be
factorised into two brackets as shown.
!! + ! − 6 = (! + 3)(! − 2)
4. Complete the question by rewriting
the original equatio into factorsied
form.
4!! + !4! − !24 = 4(! + 3)(! − 2)
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Question 50: C –
! !!!
!!!
Steps
Working
1. Write out the equation.
x ! − 25 x + 5
÷
x+5
5
2. Change the division sign to the
multiplication sign. This will swap the
position of numerator and that of the
denominator.
x ! − 25
5
×
"
x+5
x+5
3. Factorise the numerator of the 1st
term by using the difference of square
rule.
!! − !! = ! + ! ! − !
! ! − 25 = ! ! − 5! = (! + 5)(! − 5)
4. Rewrite the first term using the
factorised form.
(! + 5)(! − 5)
5
×
x+5
x+5
5. Cancel out the common factor. In
this case (x+5) can be cancelled out.
And simplify it to answer the question.
!−5
5
5 !−5
×
=
1
!+5
!+5
Question 51: B – ! !"# !"°
According to the figure, dimensions of adjacent and hypotenuse are given along with
an angle so to calculate the base from the perpendicular and angle tan !is the only
choice, hence the option with tan ! is selected.
Question 52: D – (3, -5)
Since the turning point of the line is located in the 4th quadrant where x is positive and
y is negative, the only option D can be the answer with the most appropriate set.
Question 53: A – !!! − ! = !"
According to the conditions given in the statement, option A verifies them all since in
the equation, the supposed number “x” is being subtracted from three times its cube
with the answer being 50. Hence option A is the correct answer.
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Question 54: B – !, ! , !, !
Steps
Working
1. Write down the two equations.
!! = ! ! !
! = 4! − 3
2. To find the intersections between two
functions, let ! = ! ! equal to ! = 4! − 3!
Substitute"! = ! ! !into!! = 4! − 3."
3. Rearrange the equation so that all the
terms are on the left hand side, leaving
only 0 on the right hand side.
! ! = 4! − 3
! ! = 4! − 3"
! ! − 4! + 3 = (4! − 3) − 4! + 3
! ! − 4! + 3 = 0
4. Use the cross method to factorise the
equation.
! ! − 4! + 3 = 0
!!!!!!!!!!!!!! − 3
!!!!!!!!!!!!!! − 1
−3! + −! = −4!
(! − 3)(! − 1) = 0
5. Use the null factor theorem to find the
solutions.
!−3 !−1 =0
! = 3!!"!1
Therefore option B which contains 3 and
1 as x-coordinates of the intersections is
the answer.
Question 55: B – Shop A
According to the graph, Shop A sells at the highest price for the lowest weight hence
it has the worst ratio for customers.
Question 56: C – Shop A and B
According to the graph, Shops A and B charge different prices for the same weight.
Question 57: C – Shop E
According to the graph, Shop E would provide 5 kg more for the same price than
Shop A.
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115"
Question 58: D – Shop F
According to the graph Shop F will give the best weight to price ratio to customers.
!
Question 59: B – !"# !
"
Since the angle to be calculated is located in between the adjacent and the hypotenuse
so we can make use of cosine function, cosine = !
most appropriate one."
!"#$%&'(
!"#$%&'()&
, hence option E is the
Question 60: A – ! + ! ! − !
Steps
Working
1. Write out the equation.
!"! + ! ! ! ! − !"! − !!"
2. Group !" + ! ! and −!" − !"
together.
!"! + ! ! ! + (−!"! − !!")"
3. Factorise each bracket by taking out
the highest common factor within the
bracket.
!"! + ! ! ! + (−!"! − !!")
Between xy and y2, y is the HCF
Between –xz and –yz, the HCF is –z.
! ! + ! − !(! + !)
4. This can be further factorised using
the rule.
! !+! +! !+! = !+! !+!
(! − !)(! + !)
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
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READING COMPREHENSION
EXAM PAPER 2
Detailed Solutions
Question 1: B - inevitable
The fact that he had been “doomed from the beginning” suggests that his fate was
inevitable, or bound to happen.
Question 2: C The examples given in the text are of people who believe that the places in which they
are currently located have been ‘duplicated’ or reproduced in different places. This
matches the definition of reduplicative paramnesia as “the delusional belief that a
place or location has been duplicated or that it has been relocated to another site”
Question 3:
1. Option A is not true: In the examples given, the patients are able to rationalise
(e.g. that it would be strange for there to be two Jamaica Plains Hospitals)
2. Option B is not true: The examples give the impression that the patients are
able to calmly answer questions about their locations.
3. Option C is true: The fact that patients are treated at a Neurobehavioural
Centre, as well as the fact that reduplicative paramnesia is delusional belief
with no stated physical side effects, suggests the condition is psychological.
4. Option D is not true: The patient in the first example was being treated at a
Neurobehavioural Centre
Question 4: C
The examples given in the text are of people who believe that the places in which they
are currently located have been ‘duplicated’ or reproduced in different places. This
example matches the definition in the sense that the picture is believed to have been
‘duplicated’ (rather than the person being shown the same picture twice.)
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Question 5: D
Esperanto is said to allow access to information and participation in conversations (“It
was meant to enable broad strata of society in all countries to communicate directly”),
suggesting options A and B are correct. Option C is also correct (“Esperanto can also
be learned in around a third of the time needed to learn the most commonly studied
foreign languages”). Option D, however, is not, as no mention is made in the text of
the language being based in English: in fact, it suggests that it has more in common
with Spanish or Italian (at least in the pronunciation).
Question 6: C
•
•
•
•
Option A is not true: Currently “tens of thousands” of people know Esperanto,
which suggests it will not be a global language soon.
Option B is not true: The text states that learning Esperanto is possible in a
“third of the time needed to learn the most commonly studied foreign
languages”, but does not make this conditional upon already knowing a
foreign language
Option C is true: Language is “a means by which all can engage in equitable
communication across language boundaries.”
Option D is not true: The phrase “thought by many to be the de facto world
language” suggests the author does not agree this is so.
Question 7: C
Dr Zamenhof intended for Esperanto to “be introduced as an international second
language for everybody”, suggesting that option C is correct.
Question 8: B
•
•
•
Nouns have the ending “o” and plurals are formed by adding the letter “j”:
thus, children would be written as “infanoj”
Adjectives end in “a”; superlative forms are made with “plej” (the English
word “most”): thus, biggest would be written as “plej granda”
Verbs do not change for person or number: all past tense verbs end in “is”:
thus, the past tense of “esti” would be written as “estis”.
Question 9: D
Smog is made of fog and industrial smoke which contains chemicals. The best option
is therefore ‘contaminate’, which means to make something impure due to pollution
or poison.
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Question 10: B
The poem is filled with advice from one person imparting their life experience to
someone with lesser experience e.g. from a father to a son. This is supported by the
last line ‘you’ll be a Man, my son!’
Question 11: B
“Risk it all” suggests that one should take great risks in life. “Start again at our
beginnings” suggests one should start over; “never breathe a word about your loss”
implies that one should not complain.
Question 12: A
The son is encourage to “talk with crowds” and “walk with Kings” (that is, get to
know others and their points of view) but also warned to “keep your virtue”, never
“lose the common touch” which implies he should stay true to himself.
Question 13: C
Stanza 1 suggests the son should trust himself; Stanza 2 suggests he should have
dreams, though realistic ones (“if you can dream – and not make dreams your
master”) and Stanza 3 suggests he should recover from failures without complaint.
Question 14: E
The proverb “grumbling makes the loaf no larger” suggests that complaining about
something is not going to fix the problem. None of these phrases have a similar
meaning:
•
•
•
•
Option A means that if you use something sparingly, you’ll have it longer
Option B means that taking your time is better than rushing
Option C means preventing a problem is better than reacting to one
Option D advises against judging something by its size
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Question 15: B
•
•
•
•
Option A is highly unlikely.
Option B: although no clues are given, this option seems more likely when
compared to the other options.
Option C: This is more likely to be a 21st century option rather than an 18th
century one. Also, Gulliver has come to a strange new land, whereas a crosschannel ferry would operate in familiar waters.
Option D: pirates are not mentioned in the extract, nor are any injuries which
could possibly have been incurred while fighting.
Question 16: C
The word ‘ligatures’ has the same meaning as ‘bindings’, that is, something strong
enough to hold Gulliver down. Option C is correct.
Question 17: A
•
•
•
‘… but then I knew not what they meant.’ ‘Then’ refers to time past, implying
that some time afterwards he found out what the words meant. Option A is
correct.
Options B and D give no hint as to what happened later on.
Option C: Gulliver’s sleep happened earlier. The extract describes the time
after Gulliver woke, but there is no clue as to later events.
Question 18: D
Gulliver is wondering how many of the little men there are, so ‘conjectured’ has a
similar meaning to ‘speculated’. Option D is correct.
Question 19: C
In 18th and 19th century fiction, it was common for authors to appeal to their readers,
so Option C is correct.
Question 20: B
Option B is correct: ‘Abstemious’ can mean ‘tee-total’ (a tee-totaller does not drink).
However, in this poem it has a different meaning, that of serious or solemn. The poet
is referring to himself as someone whose behaviour is proper, although we find later
he is a little more humorous than he first lets on.
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Question 21: C
Even though he has to watch over him, the poet feels sorry for his servant because his
fit lasts for ten days. The word ‘wretched’ in this context means ‘pitiful’ rather than
the modern usage of a person who is a nuisance or problem. Therefore Option C is
correct.
Question 22: A
•
•
•
Option A is correct as it maintains the rhythm and makes sense.
Options B and C do not make sense.
Option D does not maintain the rhythm.
Question 23: D
A ‘trifling jest’ means the same thing as a ‘little joke’, and makes sense in the context
of the poem. Therefore Option D is correct.
Question 24: D
•
•
•
Options A and B: these tasks are only a small part of the servant’s duties.
Option C is unlikely as it implies the servant is as educated as his master.
Option D covers all of the duties of a man-servant, so is correct.
Question 25: C
The cartoon’s message, as indicated in the final panel, is that people often use the
concept of “destiny” to avoid responsibility: they say that if something happens it will
be because it was “destiny”, not because they worked hard. Options II and III reflect
this concept: in both, the person is waiting for something (a true calling, to be offered
a job) rather than going out and taking steps to achieve their goal.
Question 26: C
“Fate” is another word for “destiny.”
Question 27: C
•
•
•
The first letter in the sentence needs to be capitalised.
The sentence is a statement so the end punctuation mark should be a full stop.
‘tired from the long mission’ is extra information about the agent, so should be
separated from the rest of the sentence with commas.
Therefore, the only correct option presented is that of option C.
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Question 28: E
The term ‘excavate’ means to dig up or remove. All the presented terms are
synonyms. This makes E is correct option.
Question 29: D
Jack is unable to control his emotions and allows them to take hold or become his
‘master’ when he is angry and seems to forget what he knows to be right. This means
something outside of what he knows is his master.
Question 30: E
Jack knows what he should or should not do, but when angered he retaliates or gets
back at the one making him angry without thinking. This means that his temper is
controlling him instead of him controlling his temper.
Question 31: D
Though the small wooden arrows were dangerous in and of themselves, it was the
force with which they flew that was most dangerous. Therefore, option D.
Question 32: C
The little boy wants to make his mother proud by becoming the man she wants him to
become, a good man.
Question 33: E
In line 16 of the poem it is clearly started that ‘rough struggles’ make men.
Question 34: B
The boy in this poem seems determined and willing to do what is needed to become a
man, even walk in bad weather to attend school.
Question 35: D
While unpaid is not an exact antonym for compensated, it is the closest appropriate
answer. Compensated means to be paid for a job that has been or will be completed,
unpaid means working for no compensation.
Question 36: B
A portal is a doorway or opening, in this case a passage into another dimension.
Option B is the only option.
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Question 37: B
Options A and C are too literal: a proverb is moral applicable to many different
aspects of life. Option D is also wrong, as the proverb compares meat and poison,
rather than saying they are the same. Thus, B is correct: something that is liked by one
person (meat) may be disliked (poison) by another.
Question 38: C
Option A is incorrect, because Ben acted for his commanding officer, implying he is
still inferior. Option B is incorrect, as Ben was given the promotion for his
“wonderful work”. There is nothing to suggest the close relationship Option D
implies. Option C is correct because assistant is a positive job, whilst still being
subordinate to the position of commanding officer.
Question 39: C
The first line (“late lies the wintry sun a-bed”) introduces the subject of the stanza
immediately; thus, the second line (“a frosty, fiery sleepy-head”) continues the
reference to the sun. In addition, the contrast of “frosty” and “fiery” is a clear
reference to the sun in winter.
Question 40: D
Options A (“burns my face”), B (“warm my frozen bones”) and C (“shivering”) all
evoke a physical response from the reader because they appeal to touch. Option D,
however, refers only to the colour of the narrator’s steps.
Question 41: A
The author believes that winter is harsh (e.g. “shivering”, “frozen bones”, “burns my
face”) but also acknowledges its beauty (e.g. “frosted like a wedding cake”). Option B
is incorrect because there is nothing to suggest the author is irritated by winter;
Option C is too overwhelmingly positive.
Question 42: A
The sun is directly referred to as a “blood red orange”. This is a metaphor, as
metaphors make direct comparisons between one thing (the sun) and another (a blood
red orange). It is not a simile, as similes use “like” or “as” to compare two things
(“the sun was as bright as a blood red orange”). It is not an example of
personification, as this technique requires a non human thing to be given a human
trait. It is not an example of exaggeration, as exaggeration requires something to be
given enhanced qualities.
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Question 43: B
The main concern of this passage is about the difference between schools with plenty
of resources (paragraph 2) and those without (paragraph 1). Option A is incorrect as,
while the wealthy school is in the inner city, the location of the poorer school is not
disclosed. Option C is incorrect as both schools seem interested in music and theatre.
Option D is incorrect as Catholic schools are not mentioned in the piece.
Question 44: C
Option A is incorrect, as it is clear both schools in the example are focused on the
arts. Option B is not supported by the article, and the suggestion that “all funds”
should be spent on creative projects seems exaggerated. Option D is incorrect as it is
too specific – there is nothing to suggest that wealthy schools cannot be diverse too.
Option C, therefore, is correct: the author clearly believes there should be a fairer
distribution of wealth between schools, given the clear differences in the ability of the
two schools mentioned to fun arts projects.
Question 45: A
“It’s imperative to have a full stop between two sentences. Otherwise, they’ll not
make sense.”
Option A is the only answer that contains:
•
•
•
•
An apostrophe in It’s (to indicate it is)
A full stop between sentences and otherwise (this is the point at which the
first sentence ends and the second begins.)
A comma after otherwise (to indicate that this is an introductory word)
A full stop after sense (to indicate the end of the second sentence)
Note that it is also possible to separate two complete sentences using a semi-colon, as
in Option E. However, this sentence lacks a comma after “otherwise” and is thus
incorrect.
Question 46: C
Option A shifts to the past tense (“excelled”), while the original sentence is in the
present tense (“is”). Option B uses a comparative word (“but”) while the original
sentence uses an adding word (“not only”). Option D implies Cathy’s singing is the
result of her academics (“since”), which is not suggested in the original sentence.
Option C, however, retains the same tense and uses an adding word (“and”).
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Question 47: C
The author’s tone describes how they feel about their subject. It is not admiring
(Option A) as the phrases “tired town”, “red slop”, “black dog suffered” all have
negative connotations. It is not critical (Option D) or attacking (Option B), however,
as the author is not passing judgment on these things – she is stating how life is in this
town. Thus, Option C is correct, as the author is clearly weary of the town and of the
atmosphere within it.
Question 48: C
While there are references to the other senses, this passage mostly appeals to touch as
the focus is on the heat of the town.
Question 49: C
Option A is too broad, as the government’s policies are not being criticised. Option B
is clearly incorrect, as the opposite is implied by the sarcastic phrase “Who taught you
how to behave?” Option D is also incorrect, as the author is implying we should
expect more from our politicians, not that we expect too little. Option C is correct, as
the phrase “Who taught you how to behave?” is commonly said to naughty children at
school: by saying it to politicians, the cartoonist implies the politicians are acting like
kids.
Question 50: B
The comment made by the spectator is sarcastic. The question is rhetorical in that the
answer is obvious and doesn’t need to be answered. The speaker in the cartoon is
therefore using sarcasm to show that the politicians are acting like children and don’t
know how to behave.
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
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NUMERICAL REASONING
TEST 3
Worked Solutions
Question 1: C – 5 hrs
Thomas is able to clean 4 offices per hour (60 min ÷ 15 min/office = 4 offices). His
wife is able to clean twice as fast, so that means she can clean 8 offices per hour.
Together, they can clean 12 offices per hour. In five hours, they can clean 60 offices
(12 x 5 = 60).
Question 2: D - 76
The sequence is formed by adding the two previous numbers together to get the next
number. Thus, the sequence would continue: 1, 3, 4, 7, 11, 18, 29, 47, 76 …
The ninth number in the sequence is 76.
Question 3: A - 24
The numbers double as you move down or to the right. Each of the open boxes have
the number 12 beside and above. Doubling that number would produce 24.
Question 4: B - 50
Jim is 50 years old. To solve, create a series of equations, then substitute back in
appropriately:
J = 2B
B = (5/8)S
S = 2G
G=B–5
Thus:
B = (5/8)(2G) = (5/8)(2)(B – 5)
B = (5/4)(B – 5)
4B = 5B – 25
B = 25
J = 2B = 2(25) = 50 years old
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Question 5: E – None of these
x represents the difference in age between the first two brothers. This would mean
that the difference in age between the second and third brothers is 2(x), between the
third and fourth is 2(2x) = 4x, and so on:
x + 2x + 4x + 8x = 15x
15x = 30 (there is a total of 30 years difference in age from youngest to oldest)
x = 2 years
35 – 8x = 35 – 16 = 19 years old (Subtracting the 8x difference from the oldest age)
Question 6: B - E
To find the number or letter that should be in the square marked by the question mark
you must carefully inspect the pattern formed by the existing numbers and letters and
make some assumptions.
In the grid you can assume that if all the numbers and letters were in place they would
form an L-shaped pattern i.e.╚. It appears the letters are consecutive .i.e. in the
normal order of letters in the English language whilst the numbers remain the same
for any pair of row-column.
Following from assumptions and observations you could start with the first columnsixth row. The consecutive letters A-K in the first column-sixth row together will
form an L-shaped pattern. For the second column-fifth row we would have the
number-9 throughout forming the L-shaped pattern. It follows from there that the Lshape formed out of the third column-fourth row would have consecutive letters A-G
filling seven squares to form the L-shaped pattern, therefore the square marked by the
question mark would have the letter “E”. The correct answer is B.
Question 7: E – None of these
Jeremy works for 7.5 hours (8.5 hrs – 1 hr lunch break). 300 boxes in 7.5 hours
amounts to 40 boxes per hour. In order to assemble 100 boxes, it would require 2.5
hours, which is 150 minutes.
Question 8: A – 1.7 m
Frank is 1.2 m tall. William, therefore, being 35 cm shorter, is 0.85 m. Since Roger
is twice as tall as William, that makes him 1.7 m tall.
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Question 9:E – None of these
Each dimension is 5 times as long. Thus, to fill the bottom surface, it would take 5
rows of 5 blocks, which is 25 blocks. Then, you would have to stack 5 of those
layers on top of each other to fill the bin. 25 blocks x 5 layers = 125 blocks.
Question 10: C – 50, 2
The relationship of each pair of numbers is that they have a common product of 100.
50 x 2 = 100.
Question 11: A. -10
The absolute value of each consequential number in the sequence is two less than the
previous number. The numbers alternate between positives and negatives. The
previous number was positive 12. Therefore, the next number must be negative and
have an absolute value of 10.
Question 12: C – 120,000
When Cody was born, his hometown was 15,000 people. After 20 years, the
population had doubled 4 times. That means that the original 15,000 doubled to
30,000, then to 60,000, then to 120,000, then to 240,000. Cody’s new town is half the
population after 20 years, which means it is half of the 240,000, or 120,000 people.
Question 13: C – 42 degrees
Steps
1. Let x equal the first integer. Find
an expression for the other two
integers. Because they are all odd, the
second integer will be 2 more than
the first, and the third will be 4 more
than the first.
2. Put the information “the product of
the first and second integers is 2 more
than the third integer” into an
equation.
3. Factorise and solve for x to find the
value of the first integer.
Working
1st integer = x
2nd integer = x + 2
3rd integer = x + 4
1st integer + 2nd integer = 3rd integer + 2
x (x + 2) = (x + 4) + 2
x2 + 2x = x + 6
x2 + 2x = x + 6
x2 + x – 6 = 0
(x + 3)(x – 2) = 0
So, either
x+3=0
x=-3
or
x–2=0
x=2
We know that x must be an odd number, so x
= - 3.
4. Add 4 to find the value of the 3rd integer = x + 4
largest (3rd) integer.
= -3 + 4 = 1
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Question 14: B - $386.50
Buy each item from whichever store sells it the cheapest.
10 shirts = 10 ($14.75) = $147.50
8 pairs of pants = 8 ($21.00) = $168.00
2 pairs of shoes = 2($35.50) = $71.00
This amounts to a total cost of $386.50.
Question 15: D – 2/9
There are 10 walnuts. There are 20 chestnuts (twice as many). There are 60 hickory
nuts (3 times as many as the chestnuts). There are a total of 90 nuts. 20 of them are
chestnuts. 20/90 reduces to 2/9.
Question 16: B - 2
With the new players, there are a total of 24 players. To divide evenly into three
teams, each team should have 8 players. Taking 2 players away from the original two
teams would give those teams 8 players each. The 4 newcomers would be given 4
additional players and have a total of 8 players as well.
Question 17: C – 23
Subtracting the 54 copper coins and the 38 bronze coins from the total of 125 coins
leaves us with a total of 33 silver coins in the jar. 75 of the coins are counterfeit. At
most, 27 of the copper coins are counterfeit. At most, all 38 bronze coins are
counterfeit. If that is so, then that leaves 10 more coins that must be counterfeit.
These would have to be silver coins. Thus, the greatest number of legitimate silver
coins that the jar might contain would be 23.
Question 18: E
One elephant tusk = 3 lion skins. 3 lion skins = 30 baskets. 30 baskets = 150 m of
rope.
Question 19: D - $6.70
There are a total of 40 minutes of talking. 2 of those minutes are charged at the rate
of $0.50 because they are first minutes of calls. 38 of the minutes are charged at the
additional minute rate of $0.15. Thus, 2($0.50) + 38(0.15) = $6.70.
Question 20: A - 7
The correct answer is A. Using decomposition you can show place values of “digits”:
MN + N = NM - N
10M + N + N = 10N + M - N
10M + 2N = 10N – N + M
10M - M
= 9N – 2N
9M
= 7N
Using simple inspection trial and error (on equation 9M = 7N) with the possible
answers, M can only be equal to 7 and therefore N will be equal to 9.
Checking: 79 + 9 = 97 - 9
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Question 21: E – None of these
The office clock is 18 minutes slower in all.
Since the bus leaves at 5:19 pm, you have to leave the office at 5:07pm.And because
the office clock is 18 minutes slower in all, it will read 4:49pm when it is actually
5:07am.
Question 22: C - 124
Steps
1. Define the variables.
2. Given the difference of two
numbers is 10 and their
product is 12
3. Determine the formula to find
the sum of squares of the
given two numbers.
4. Use the difference of two
squares rule
5. Rearrange the rule to make
a2 + b2 the subject
6. We know ab = 12 and
a-b = 10. Substitute into the
formula to find the sum of the
squares of the given two
numbers
Working
Let a and b represent the two numbers
a – b = 10
a!× b = 12
a2+ b2 = ?
(a - b)2 = a2 + b2 – 2ab
a! + b! − 2ab
a2+ b2 = (a − b)!! + 2ab
a2+ b2 = (a − b)!! + 2ab
a2+ b2 = 10!! + 2(12)
a2+ b2 = 100 + 24
= 124
Question 23:D – 16 litres
Steps
1. Subtract ¼ from 7/8 to find how much
petrol has been added
2. Formulate an equation making x = the
total capacity of the tank
3. Multiply both sides by 8
4. Divide each side by 5
Working
7 1
−
8 4
7 2
= −
8 8
5
=
8
5
x = 10 litres
8
5x = 80 litres
x = 16 litres
Question 24: A - 20
If the numbers add to 60, then U + W = 30. Remember U = 2W.
Substitute U = 2W into U +W = 30:
2W + W = 30
3W = 30 ∴ W = 10 and so U = 20.
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Question 25: C – 10 minutes late
His usual routine is to leave 1 hour before school starts. Today, he leaves 30 minutes
later than usual, which means he leaves 30 minutes before school starts. 20 minutes
of driving plus 15 minutes for breakfast plus another 5 minutes of driving is a total of
40 minutes. Thus, he will arrive 10 minutes later.
Question 26: A
145 fence rails at $87 is equivalent to 5 fence rails for $3 (divide each number by 29).
55 fence rails is eleven sets of 5, which would thus cost $33.
Question 27: B - 2
By adding the numbers on the diagonal, we get a total of 21. By filling in the missing
numbers, we have X equal to 2. The correct answer is B.
Question 28: E – None of the above
Adding the two categories of students above 70 for each test gives totals of 22, 23, 24,
and 22. The average of those numbers is 22.75, which is not one of the given
answers.
Question 29: C - 26
All the numbers except 26 are perfect squares when divided by 2.
Question 30: D
Let x represent the unknown distance that the same car can cover on a full tank.
The ratio statement is:
!"#!!"
!!!"#$%&
so the proportion is:
!"#!!"
!!!"#$%&
!!!"
= !"!!"#$%&
Solve for x by cross multiplying fractions:
!"#
!
!
= !"
6x = 120 × 60
6x = 7200
x = 7200/6
x = 1200
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Question 31: A – 2x -1
If you double the previous number and subtract 1, you will have the given sequence.
That is expressed by 2x – 1.
Question 32: A - $5
Write out the information available in the manner below and that would make the
problem easier to solve.
60
50
ostrich*eggs
coconut*corn*bread
lobsters
135
$30
$1,800
$15
2,425
60 ostrich eggs cost $30 each and so it would cost $1,800 in all.
The grocer bought 50 loaves of coconut corn bread.
With the knowledge of these two quantities 60 + 50 = 110 we are able to work out the
quantity of the third item, lobsters i.e. 135 – 110 = 25 .With that quantity we are able
to calculate the total cost of lobsters 25 × $15 = $375. With knowledge of the total
cost of ostrich eggs($1,800) and lobsters ($375) we can compute the total cost for
50 loaves of coconut corn bread i.e. $2,425 - $1,800- $ 375 = $250. $250 ÷ 50
= $5 –price for each loaf of coconut corn bread.
Question 33: C - $6
Buying each coffee and donut separately would cost 12 ($3.00) + 18 ($1.50) = $63.00
Buying 12 combinations and the remaining 6 donuts would cost:
12 ($4.00) + 6 ($1.50) = $57.00. This is a savings of $6.
Question 34: D - $30
20% off the original $50.00 price would be $40.00. Then, taking 25% off the new
price, we would have $30.00.
Question 35: B - 5
(x+3)2 = 102 – 36; (x+3)2 = 64; x + 3 = 8; x = 5
Question 36: E – None of these
The rate of water coming into the pool can be expressed as 1/20 of the pool per
minute. The amount of water leaving is 1/40 of the pool per minute. The net gain,
then, is 1/20 – 1/40 = 2/40 – 1/40 = 1/40 pool per minute. At that rate, it will take 40
minutes for the pool to be filled.
Question 37: A - $50
Peter pays a total of $50 for 200 ice cream sandwiches. He takes in a total of $100
when he sells them all. The profit is $50.
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Question 38: C – 5 hours
The first train travels for 30 minutes before the other starts, which is half an hour.
½ h (60 km/h) = 30 km
This gives it enough time to travel 30 km before the other train begins.
The second train travels 6 km/h faster than the first train and thus gets 6 km closer
every hour.
(30 km) / (6 km/h) = 5 hrs
It will take 5 hours for the second train to make up the 30 km difference.
Alternatively, describe the distances of the trains with two equations, set them equal,
and solve:
x = 60(t + 0.5)
60(t + 0.5) = 66t
60t + 30 = 66t
30 = 6t
t=5
y = 66t
Question 39: E – None of these
distance = rate x time
d = 50 km/h x 1 hr = 50 km
(50/2 km) /(25 km/h) = (25 km) / (25 km/h) = 1 hr
If Hank drives half way home at half his normal speed, it will take him just as long as
it usually does to get all the way home. He cannot get home in his usual time no
matter how fast he drives.
Question 40: D - $120
When we subtract the cost of two tables ($50 each means $100) from the total
payment, we have $210. The desk is equal in cost to 8 chairs. Those 8 chairs plus the
6 chairs that Barry bought must have cost $210. 14 chairs = $210. 1 chair =
($210)/14 = $15. The desk cost as much as 8 chairs, so $15 x 8 = $120.
Question 41: B – 34
The sequence alternates between subtracting one from the previous term and doubling
the previous term. Because we have just subtracted one, it is now time to double the
term. Doubling 17 results in 34 as the next term.
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Question 42: C - 45
There are x red beads and x white beads. There are 3x green beads. There are 5x
yellow beads. There are 5x purple beads.
x + x + 3x + 5x + 5x = 15x
Altogether, there are 15x beads.
15x = 135 beads
x = 9.
There were 5x purple beads, so 5(9) = 45 purple beads.
Question 43: D - $120
A cheese pizza is $10. A pepperoni pizza is 20% more, which amounts to $12. A
supreme pizza is 25% more than the pepperoni pizza, which amounts to $15.
3 cheese pizzas = 3 x $10 = $30
5 pepperoni pizzas = 5 x $12 = $60
2 supreme pizzas = 2 x $15 = $30
In total, the order cost $120.
Question 44: C - 114
84 goals in 28 games is a rate of 3 goals/game. Multiplied out by a full 38 games is
114 goals.
Question 45: B – 27
For each unit of 3:7, there is a difference of 4 between the two terms. The problem
tells us that there is a total difference of 36 between the two terms. That would mean
we need 9 units of that ratio. Thus, multiplying the ratio of 3:7 by 9, we have 27:63.
That is a difference of 36, as needed. There are 27 pigs.
Question 46: A – Runner 12 ran the race 5 minutes faster than runner 8
Runner 12 is four runners after runner 8. This means that runner 12 must have started
the race 8 minutes after runner 12. There is only 3 minutes of difference between
when the two runners finished the race. This means that runner 12 must have run the
race 5 minutes faster than runner 8.
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Question 47: D – 30
The fact that the class can be divided evenly into three groups means the number of
students must be a multiple of 3. Likewise, if they can sit evenly in rows of 5 desks,
it must be a multiple of 5. 15 would fit those two requirements, as would any
multiple of 15. Ned knows there are more than 20 students, but fewer than 35. 30 is
the only multiple of 15 within that range.
Question 48: D
½ x = 2x – 15
x = 4x – 30
0 = 3x – 30
30 = 3x
10 = x
Question 49: B – 2, 3
Let the numbers be "a" and "b"
Equations:
1/a + 1/b = 5/6-Eq.1
1/a - 1/b = 1/6-Eq.2
Add the 2 equations to get:
2/a = 1
a=2
Solve for b:
1/a + 1/b = 5/6
1/2 + 1/b = 5/6
1/b = 5/6 - 3/6
1/b = 2/6
b=3
Question 50: C – Company C
The total for each company would be:
Company A: 20($25.50) + 30($32.75) + 50($6.25) = $1805.00
Company B: 20($22.50) + 30($33.25) + 50($7.50) = $1822.50
Company C: 20($22.75) + 30($35.75) + 50($4.25) = $1740.00
Company D: 20($30.50) + 30($29.75) + 50($5.75) = $1790.00
Company E: 20($29.50) + 30($31.50) + 50($5.25) = $1797.50
The lowest price is with company C
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
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VERBAL REASONING
EXAM PAPER 3
Detailed Solutions
Question 1: A - Yield
Capitulate, relent and surrender are all verbs that mean to give up. Yield is also a verb
that means to give up.
Question 2: A - Irrelevant
Peripheral, unrelated and extraneous are all adjectives to describe something that is
not related or relevant. Irrelevant means the same thing.
Question 3: B – Me
My mother’s father’s only daughter is my mother. My mother’s only child is me.
Therefore, I must be Gary.
Question 4: B – 1, 3 and 5
If Laura and Ian are siblings (statement 5), and Laura is taller than everyone in her
family (statement 3), then Laura must be taller than Ian. If Ian is tall (statement 1),
then Laura must also be tall. None of the other statements prove that Laura is tall.
Question 5: D - Withdrawn
Antisocial is an adjective that describes someone who doesn’t like socialising with
people. Withdrawn is also an adjective that describes someone who doesn’t like
socialising.
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Question 6: B – Some FOOTs are FLITs
The answer can be found using a Venn-diagram.
A is false because some FRUITS are FOOTS.
C is false because only some FEETS are FRUITS.
D is false because only some FOOTS are FLITS.
B is true because some FOOTS are FLITS.
Question 7: D – Jeremy and Isabella
Jeremy takes 6 steps forwards and 2 steps back. He is 4 steps from the line.
Paul takes 4 steps forwards and 2 steps back. He is 2 steps from the line.
Isabella takes 8 steps forwards and 4 steps back. She is 4 steps from the line.
Ian takes 3 steps forwards and 2 steps back. He is 1 step from the line.
Jeremy and Isabella are furthest from the line.
Question 8: A - patience
Disrespect, courtesy and compassion are all nouns to describe ways that you can treat
people. Patience is also a noun to describe a way you can treat people. Tease and
provoke are verbs. Cruelly is an adverb.
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Question 9: B - ittleyoo
ittle
nattle or yoo
Means dog, as it appears in the first and last word.
One of these must mean lap, as they appear in the second word.
So, the word for “lap dog” must contain the word ittle and either nattle or yoo.
Answers B, C and D match these requirements.
However, when we look at the first and second words, we notice that word order is
reversed in the obscure language. The word ittle comes first in each phrase, while the
word dog comes second in the English translation. Following this pattern, the word
for “lap dog” should start with ittle and end with yoo.
Question 10: C – Wild is to feral
Domestic is a synonym of tame. Wild is a synonym of feral. Therefore, domestic is to
tame as wild is to feral.
Question 11: C – Some RUGS are JUGS
The answer can be discovered through elimination and the use of a Venn diagram.
A is false because only some PUGS are RUGS.
B is false because all BUGS are RUGS.
D is false because some JUGS will be RUGS.
C is true because some RUGS are JUGS.
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Question 12: B – 1 and 4
If I like the colour of Lily’s hair (statement 1) and Lily has black hair (statement 4),
then I must like the colour black.
Question 13: D – Wednesday
Draw up a table and fill it in with each piece of information. Firstly, we find out that
Bob doesn’t do trapeze or perform on Thursday.
Day
Bob
Rob
Job
Zob
Lob
Juggling
Swordswallowing
Lion
taming
Trapeze
Magic
✕
M/T/W/F
M/T/W/Th/F
M/T/W/Th/F
M/T/W/Th/F
M/T/W/Th/F
Next, we learn that Rob is the juggler, but doesn’t perform on Monday or Friday.
Day
Bob
Rob
Job
Zob
Lob
Juggling
✕
✓
✕
✕
✕
M/T/W/F
T/W/Th
M/T/W/Th/F
M/T/W/Th/F
M/T/W/Th/F
Swordswallowing
✕
Lion
taming
Trapeze
Magic
✕
✕
✕
✕
We know that Job performs on Friday and does not swallow swords.
Day
Bob
Rob
Job
Zob
Lob
Juggling
✕
✓
✕
✕
✕
M/T/W
T/W/Th
F
M/T/W/Th
M/T/W/Th
Swordswallowing
✕
✕
Lion
taming
✕
Trapeze
Magic
✕
✕
✕
We know that the magic act takes place on Friday, so Job must be the magician.
Day
Bob
Rob
Job
Zob
Lob
Juggling
M/T/W
T/W/Th
F
M/T/W/Th
M/T/W/Th
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✕
✓
✕
✕
✕
Swordswallowing
✕
✕
Lion
taming
✕
✕
Trapeze
✕
✕
✕
Magic
✕
✕
✓
✕
✕
139"
We know that the lion is tamed every Tuesday. This means that Rob and Job, who
aren’t lion tamers, can’t perform on Tuesday.
Day
Bob
Rob
Job
Zob
Lob
Juggling
✕
✓
✕
✕
✕
M/T/W
W/Th
F
M/T/W/Th
M/T/W/Th
Swordswallowing
✕
✕
Lion
taming
✕
✕
Trapeze
✕
✕
✕
Magic
✕
✕
✓
✕
✕
Finally, we know that Lob always performs on Thursday. This must mean that Rob
performs on Wednesday.
Day
Bob
Rob
Job
Zob
Lob
Juggling
M/T
W
F
M/T
Th
✕
✓
✕
✕
✕
Swordswallowing
✕
✕
Lion
taming
✕
✕
Trapeze
✕
✕
✕
Magic
✕
✕
✓
✕
✕
Therefore, we can see that Rob performs his juggling act on Wednesday.
Question 14 : D – Spread
The letters of the word PIRATES can be rearranged to spell PARTIES, which is a
synonym for celebrates.
Question 15: D - Demand
Fastidious, acceptable and particular are all adjectives. Demand is a verb.
Question 16: C - Prevalent
Desperate is an adjective that describes an extreme need. Urgent is also an adjective
that describes an extreme need.
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Question 17: E - Monica
Add names to a list as you read each piece of information. Put the shorter students at
the bottom and taller students at the top. Firstly, we know that Ace was taller than
Fiona.
Ace
Fiona
Next, we learn that Apple was taller than Monica but shorter than Helga. However,
we don’t know whether or not they are taller or shorter than Ace and Fiona.
Ace
Fiona
Helga
Apple
Monica
We then learn that Monica was taller than Fiona. We know that Ace was taller than
only Fiona, so Monica must have also been taller than Ace.
Helga
Apple
Monica
Ace
Fiona
We then learn that, by the end of the year, Ace had moved to another class and Fiona
became taller than everyone except for Helga. The new order will look like this.
Helga
Fiona
Apple
Monica
Monica is now the shortest student in the class
Question 18: D - Believe
Distrust is a verb that means to disbelieve. The opposite to this is believe.
Question 19: D - Swollen
Engorged is an adjective to describe something that has grown too large. Swollen is
also an adjective to describe something that has grown too large.
Question 20: D – Mechanic is to car
A doctor is a person who fixes your body. A mechanic is a person who fixes your car.
Therefore, doctor is to body as mechanic is to car.
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Question 21: D – Some cows are vows
The answer can be discovered through the use of a Venn diagram.
As we can see, A is false because some vows are cows.
B is false because only some hows are cows.
C is false because only some cows are nows.
D is correct as some cows are vows.
Question 22: A – either Jarred or Kyle
This question can be answered through the use of a table. The first thing we learn is
that Jarred is not the editor.
Director
Actor
Editor
✕
Jarred
Kyle
Sam
The second thing we learn is that Sam cannot act. Therefore, Sam is not the actor.
Director
Actor
Editor
✕
Jarred
Kyle
Sam
✕
The third thing we learn is that Kyle is best friends with the editor. Therefore, Kyle is
not the editor.
Director
Jarred
Kyle
Sam
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Actor
Editor
✕
✕
✕
142"
From here, we can deduce that Sam must be the editor.
Director
Jarred
Kyle
Sam
Actor
Editor
✕
✕
✕
✓
✕
Therefore, since we have no further information, either Jarred or Kyle could be the
actor.
Question 23: A - 2
Add names to a list as you read each piece of information. Firstly, I am flanked by
Jerry and Jenny.
Jerry – Me – Jenny
Next, we find out that Jenny is flanked by myself and Joan.
Jerry – Me – Jenny – Joan
Next, we learn that there are three people between Peta and Jerry. Therefore, Jerry
must be next to Joan.
Jerry – Me – Jenny – Joan – Peta
So, if Jenny is standing to my left, there are 2 other people on my left: Joan and Peta.
Question 24: B - Comparative adjective that can be used to compare one chip to
another
When rearranged, the letters of the word RETAILS can spell SALTIER, which is an
adjective that can be used to compare one chip to another. For example: “this chip is
saltier than that one.”
Question 25: C - Syringe
Scalpel, gauze and stretcher are all things that a doctor might use in a hospital. A
syringe is also something that a doctor might use in a hospital.
Question 26: D – D
This is a trick question. Remember that if Dennis’s mum has 5 children, then one of
the children must be Dennis himself. So Dennis must be the fifth child. His name
starts with D.
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Question 27: B – Dancing is exhausting
3333 and 99
Must mean is and very, as they are the common words
in each sentence. Which one means which is not
certain.
Must mean dancing and fun, as they are the common
words in each sentence. Which one means which is not
certain.
Must mean running and exhausting, as they are the
common words in each sentence. Which one means
which is not certain.
1010 and XOXO
()() and <><>
So 1010 99 <><> must mean dancing/fun is/very running/exhausting. The only
option that matches this is B.
Question 28: A – Sorrowful is to weep
When I am angry, I shout. When I am sorrowful, I weep. Therefore, angry is to shout
as sorrowful is to weep.
Question 29: B – James and Peter
Add names to a list as you read each piece of information. Barry is ahead of Will but
behind James.
Will – Barry – James
Peter is behind Will.
Peter – Will – Barry – James
So James will win the race and Peter will lose.
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Question 30: C – Some TOCKS can be TEAKS
The answer can be discovered through elimination and the use of a Venn diagram.
A is false because some TICKS are TEAKS.
B is false because only some TACKS are TOCKS.
D is false because only some TOCKS are TACKS.
C is true because some TOCKS are TEAKS.
Question 31: D - Warm
Cool, tepid and balmy are adjectives to describe temperatures. Warm is also an
adjective to describe termperatures.
Question 32: C – 2 and 4
If Mark’s parents live together (statement 3), and Mark’s father lives with all of his
children (1), but only lives with two other people (statement 5), then Mark’s father
must only have one child. The two people that Mark’s father lives with are Mark and
his mother. Therefore, Mark is an only child. Statements 2 and 4 are irrelevant to this
proof.
Question 33: C – Football match is to stadium
A hearth is a place when you light fires. So a fire happens in a hearth. A football
match happens in a stadium. Therefore, fire is to hearth as football match is to
stadium.
Question 34: C - Impede
Create, invent, fabricate, make, produce and generate are all verbs that mean to create
or make something. Impede means to stop something, so it is the odd word out.
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Question 35: A - Flexible
Pliable is an adjective that describes something that can be changed or reshaped with
ease. Flexible is also an adjective that describes something that can be changed or
reshaped with ease.
Question 36: D – Chicken pie
The answer can be ascertained by creating a table. The first thing we learn is that
Gilly is a vegetarian, so she can’t have the steak or the chicken pie.
Steak
Gilly
Milly
Rory
Quinn
Vegetable Curry
✕
Chicken Pie
Potato chips
✕
The next thing we learn is that Rory doesn’t want the curry or the pie.
Steak
Gilly
Milly
Rory
Quinn
Vegetable Curry
✕
Chicken Pie
Potato chips
✕
✕
✕
We then learn that Milly ordered the steak.
Steak
Gilly
Milly
Rory
Quinn
✕
✓
✕
✕
Vegetable Curry
Chicken Pie
Potato chips
✕
✕
✕
✕
✕
✕
Vegetable Curry
Chicken Pie
Potato chips
✕
✕
✕
✕
✕
✕
✕
✓
✕
This means that Rory must have ordered the chips.
Steak
Gilly
Milly
Rory
Quinn
✕
✓
✕
✕
From this, we can figure out that Gilly must have had the vegetable curry, and Quinn
must have had the chicken pie.
Gilly
Milly
Rory
Quinn
Steak
Vegetable Curry
Chicken Pie
Potato chips
✕
✓
✕
✕
✓
✕
✕
✕
✕
✕
✕
✓
✕
✕
✓
✕
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Question 37: D - Angry
Pride, fury and courage are nouns. Angry is an adjective. Therefore, angry is the odd
word out.
Question 38: B – 1 and 5
If Jeremy has 8 children (statement 1), and he has four sons (statement 5), then
Jeremy must have four daughters. All of the other statements are irrelevant in this
proof.
Question 39: D – Horace and Polly
By making a map of the trip (with each box representing one kilometre), one can see
that Polly and Horace are both 2km from home.
Polly
Georgie
Horace
Suzie
Question 40: A - Precise
The word sloppy is an adjective that means messy or clumsy. Precise is an adjective
that means neat and careful. Therefore, precise is the opposite of sloppy.
Question 41: B – Clear is to plain
Remember and recall are synonyms. Clear and plain are synonyms. Therefore,
remember is to recall as clear is to plain.
Question 42: B - HOOWOO
BOO
HOO
WOO
HOO and UUUUH
Means “no”, as it is in the first two sentences.
Means “say”, as it is the other word in the first sentence.
Means “thanks”, as it is the other word in the second sentence.
Mean “oh” and “yes,” but it is not certain which one means
which.
So the word for “yes thanks” must contain HOO or UUUUH and WOO. The only
answer that fits this is B.
Question 43: C – Uninterested
Curious is an adjective to describe someone who is interested to know more about
something. Uninterested is the opposite of this.
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Question 44: D - Hero
A protagonist is the main character is a story. Hero means the same thing as this.
Question 45: B – Mrs. Henderson
Draw a circle and add names around it as you gain more information. The first thing
we learn is that Mrs. Smith is sitting between Mrs. Henderson and Mrs. Brown.
However, we don’t know who is on her left and who is on her right yet.
The next thing that we learn is that Mr. Green is opposite to Mrs. Smith and Mr.
Rowe is on Mr. Green’s left. Remember, when figuring out which side is “on the
left,” imagine that you are Mr. Green, looking towards the centre of the table.
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Next, we learn that Mrs. Brown is sitting two seats to the left of Mr. Rowe, so she
must be to Mrs. Smith’s right and Mrs. Henderson must be to Mrs. Smith’s left. We
also learn that Mrs. Brown is one seat to the left of Mr. Brookes and opposite to Mr.
Chu.
Since Mr. Black is the only person left, he must be between Mr. Green and Mr. Chu.
As we can see, Mrs. Henderson is opposite to Mr. Rowe.
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Question 46: C - 4
If Linda is a chef (statement 1) and one of Linda’s daughters followed in her footsteps
(statement 3), then one of Linda’s daughters must be a chef. If Linda is Kathy’s
mother (statement 5) and Kathy has no sisters (statement 2), then Kathy must have
been the daughter than became a chef. Therefore, Kathy is a chef. Statement 4 is not
relevant to this proof.
Question 47: B – Some FIVEs are THREEs
The answer can be discovered through elimination and the use of a Venn diagram.
A is false because some TWOs are TENs.
C is false because all, not some, TWOs are FIVEs.
D is false because only some FIVEs are TWOs.
B is true because some FIVEs are THREEs.
Question 48: D – Pliable
Powerful, effective and forceful are all adjectives to describe something with a lot of
force and power. Potent, compelling and strong all mean the same thing, while pliable
means flexible. Therefore, pliable is the odd word out.
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150"
Question 49: C – Mobility is to wheelchair
You can improve your sight with glasses. You can improve your mobility with a
wheelchair. Therefore, sight is to glasses as mobility is to wheelchair.
Question 50: B – soak is to wet
When you polish something it becomes smooth. When you soak something it
becomes wet. Therefore, polish is to smooth and soak is to wet.
Question 51: A - Clever
Witty, astute and insightful all mean smart and perceptive. Clever also means smart
and perceptive.
Question 52: D - Cataclysm
Tragedy is a noun to describe something dramatic and upsetting that has happened.
Cataclysm is also a noun to describe something dramatic and upsetting that has
happened.
Question 53: B – Meat, eat, found
EEEE
ZZZ, EEE
and Z
Must mean meat, as it is in both sentences
These words must mean I, will and eat, as they are the remaining
words in the first sentence. However, it is not certain which one
means which.
EEZZ ZEZ E These words must mean you, have and found, as they are the
remaining words in the first sentence. However, it is not certain which
one means which.
So EEEE means meat. Z could mean I, will or eat. EEZZ could mean you, have or
found. The only answer that first this is B.
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151"
Question 54: A - sneevgee
ex
sneev
gorn
bloon gee
Must mean sandwich, as it is in the first two sentences.
Must mean vegetable, as it is the only remaining word in the first
phrase.
Must mean sausage, as it is the only remaining word in the second
phrase.
These words must mean small and curry, as they are in the third
phrase. However, it is not certain which one means which.
So the word for vegetable curry must contain sneev and either bloon or gee. This
could be either be A, B or D. So the word order must be important. You will notice
that the word order of each phrase is the same as in English. For example, the word
for vegetable (sneev) comes before the word for sandwich (ex) in vegetable sandwich
(sneevex). So the word for vegetable curry should start with sneev. Only A fits this
pattern.
Question 55: A - Tiny
Minute, slight and meager are all adjectives that mean small. Tiny is also an adjective
that means small.
Question 56: A - Alan
Add names to a list as you read each piece of information. Firstly, we know that, after
the first lap, Alan was coming first. And Irene was coming after Ted, and Mary after
Irene.
Alan
Ted
Irene
Mary
Then we learn that Mary overtook the person in front of her.
Alan
Ted
Mary
Irene
Finally, we learn that Ted rushed ahead and came first.
Ted
Alan
Mary
Irene
As we can see, Alan came second.
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Question 57: B – Pria
Add names to a list as you read each piece of information. Firstly, Nia is taller than
Pria but shorter than Issy.
Issy
Nia
Pria
Secondly, Gladys and Oscar are the shortest students in the class, but Gladys is taller
than Oscar.
Issy
Nia
Pria
Gladys
Oscar
Thirdly, Zoe is standing next to Gladys. We know that Gladys is the second shortest,
so Zoe must be taller than Gladys.
Issy
Nia
Pria
Zoe
Gladys
Oscar
As we can see, Pria is the third tallest student in the class.
Question 58: D – Dangerous
Threaten, confront and challenge are all verbs that mean to pose a threat to someone
or something. Dangerous, on the other hand, is an adjective.
Question 59: B – Freed
Contained is an adjective that means restrained or held captive. Freed is the opposite
of this.
Question 60: B – Bill
This question can be solved through the use of a table. The first thing we learn is that
the baker lives with Bill. This means that Bill is not the baker.
Butcher
Will
Bill
Jill
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Baker
Candle stick maker
✕
153"
Next, we learn that Jill goes to yoga with the candles stick maker. Therefore, Jill is
not the candlestick maker.
Butcher
Baker
Will
Bill
Jill
Candle stick maker
✕
✕
Next, we learn that Will is the butcher.
Butcher
Baker
✓
Will
Bill
Jill
Candle stick maker
✕
✕
✕
✕
This means that Bill must be the candle stick maker.
Butcher
Will
Bill
Jill
Baker
✓
Candle stick maker
✕
✕
✕
✓
✕
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
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MATHEMATICAL REASONING
EXAM PAPER 3
Detailed Solutions
Question 1: E - 8
Steps
1. Use BODMAS
2. Simplify the operation
Working
6 + 12 ÷ 3 − (2 + 12 × 0)
= 6 + (12 ÷ 3) – (2 + (12 × 0))
= 6 + 4 – (2 + (0))
=6+4–2
=8
Therefore, the answer is E
Question 2: A – {1,2,4,6,10,15}
The union of two sets consists of all the elements present in both the sets
Question 3: E
Steps
Working
1. First work out how much of the $16,400 – 3750 = $12,650
loan he still owes.
2. Find out the percentage of the total 12,650 ÷ 16,400
loan
= 0.77
3. Convert to percentage
Question 4: D – x = 0.6
Steps
1. First expand the equation.
2. Collect like terms
3. Solve for x
©"SPECTRUM TUITION PTY LTD
= 0.77
= 0.77 × 100
= 77%
Therefore the answer is E
Working
2(x + 3) + 3(x – 3) = 0
= 2x + 6 + 3x – 9 = 0
= 2x + 3x + 6 – 9 = 0
= 5x – 3 = 0
5x – 3 = 0
5x = 3
x = 3/5
x = 0.6
Therefore the answer is D
155"
Question 5: A – 25 – 9b2
Steps
1. Use the Difference of Two Squares
rule:
(a + b) (a – b) = a2 – b2
Working
(5 – 3b)(5 + 3b)
= 25 – 9b2
Therefore the answer is A
2. Alternatively, you can expand the (5 – 3b)(5 + 3b)
equation but this will take a bit = 25 + 15b – 15b – 9b2
longer.
= 25 + 0 – 9b2
=25 – 9b2
Therefore the answer is A
Question 6: B - 39 + 4 2 cm
Steps
1. Split the shape into three:
A triangle on the left (1), a square in
the middle (2), and another triangle
on the right (3).
2. Start with shape (2), the square.
Working
(1)"
(2)"
(3)"
The line BC = 7cm
The length of the lines BE, EF, and Therefore:
CF should equal the line BC.
Line BE = 7cm
Line EF = 7cm
Line CF = 7cm
3. Move to shape (1), the triangle
a2 + b2 = c2
Use Pythagora’s theorem to work out
the length of AE.
a2 + 72 = 92
Let a = AE
a2 = 92 – 72
Let b = BE
a2 = 81 – 49
Let c = 9cm
a2 = 32
a = 32 cm = 4 2 cm
This is the length of the line AE.
4. You should now have all the AB + BC + CD + FD + EF + AE = total
lengths required to work out the perimeter.
perimeter of the shape.
AB = 9cm
BC = 7cm
CD = 10cm
FD = 6cm
EF = 7cm
AE = 4 2 cm
©"SPECTRUM TUITION PTY LTD
9 + 7 + 10 + 6 + 7 + 4 2 = total perimeter
= 39 + 4 2
Therefore the answer is B.
156"
Question 7: C – 20 months
Steps
1. Assign letters for the ghettoblaster
and for Jefferson, as well as for the
number of months.
2. Create expressions for both the
ghettoblaster.
Remember the price of the
ghettoblaster rises by an average $1
per month.
3. Create an expression for Jefferson.
Remember he has saved $45. He can
save a further $20 per month
4. To find out how many months it
will take Jefferson to save for the
ghettoblaster, let both equations equal
each other.
Working
Let g = ghettoblaster
Let j = Jefferson’s money
Let m = number of months
Solve for m
425 + m = 45 + 20m
425 – 45 = 20m – m
380 = 19m
m = 380/19
m = 20
g = 425 + m
j = 45 + 20m
Remember g = 425 + m and j = 45 + 20m
Let g = j,
Therefore, it will take Jefferson 20 months.
The answer is C.
Question 8: A -
233 m
Steps
1. Use Pythagoras’s theorem to solve
for the fallen part of the tree.
2. Let a = 8m
Let b = 13m
Let c = fallen part of the tree
3. Solve for c
©"SPECTRUM TUITION PTY LTD
Working
Pythagoras’s theorem:
a2 + b2 = c2
c2 = a2 + b2
c2 = 82 + 132
c2 = 82 + 132
c2 = 64 + 169
c2 = 233
c2 = 233 m
Therefore the answer is A
157"
Question 9: B – 1.8cm
Steps
1. If they are similar triangles, the
lengths of the same sides will have
the same ratio.
2. Work out the ratio of 6cm : 1.2cm
3. Solve for x
Working
9:x
6cm : 1.2cm
6cm : 1.2cm
6 ÷ 1.2
=5
9 : x (and thus 9 ÷ x) should equal 5
Therefore, 9 ÷ x = 5
x =9÷5
x = 1.8cm
Therefore the answer is B
Question 10: C . − 6 x − 17 y
Steps
1. Expand the brackets
2. Arrange like terms together.
3. Simplify.
Working
− 5(2 x + y ) + 4( x − 3 y )
= -10x – 5y + 4x – 12y
= -10x – 5y + 4x – 12y
= -10x + 4x – 5y – 12y
= -10x + 4x – 5y – 12y
= -6x – 17y
Therefore the answer is C
Question 11: A. 10
Steps
1. Write out expressions for bananas,
apples, and pears.
Working
b = bananas, a = apples, p = pears
b : a = 3:5
a : p = 4:2
2. You are told she bought 12 b : a = 3:5
bananas.
Using this, work out how many b 3
=
apples were bought.
a 5
If b = 12, then:
12 3
=
a 5
3. Solve for a.
©"SPECTRUM TUITION PTY LTD
3a = 12 × 5
3a = 60
a =20
158"
3. Now work out the number of pears a : p = 4:2
bought.
If a = 20, then:
20 4
=
p 2
Solve for p
4p = 20 × 2
4p = 40
p = 10
The number of pears bought is 10. The
answer is A.
Question 12: C - 85°
Steps
1. First work out what angle a
represents. You have enough
information to work this out.
Working
a + (a +10) = 180°
2a + 10 = 180
2a = 180 – 10
2a = 170
a = 170 ÷ 2
a = 85°
2. Now that you know what a is, you If a = 85°, then c = 85°
can easily work out what c is because
a and c are corresponding angles.
The answer is C
This occurs when two lines are
crossed by another line (which is
called the transversal). The angles in
matching
corners
are
called
corresponding angles.
Question 13: B - EF = 15
Steps
1. First work out what EF is.
You have enough information to
work out what this is.
Since they are similar triangles,
EF = AC, and DF = BC
Working
DF = BC; where DF = 45 and BC = 15
45 EF
=
15
5
45
× 5 = EF
15
EF = 15
2. Look at the options and see if any Option B matches your answer.
match EF = 15.
Therefore, the answer is B
©"SPECTRUM TUITION PTY LTD
159"
Question 14: B - 136/7m
Steps
1. This is another question using
‘similar triangles’
Working
If they are similar triangles, then the
ratio of the lengths of the same sides
are equal.
Start with the smaller triangle. Using 4 : 7 or 4
the information provided, what is the
7
ratio for two sides of the smaller
triangle?
2. Look at the larger triangle and find
the ratio for the same sides (as the Add the 7m + 27m = 34m
smaller triangle) of the larger triangle.
Therefore:
h
Remember to add the bottom lengths
together.
34
3. If we know that the ratio of the 4 = h
lengths of the same sides should be 7
34
equal, you just need to make the two
ratios equal one another and then
34 × 4
h=
m
solve for h.
7
h=
136
7 m
Therefore, the answer is B
Question 15: A – 1/12
Steps
1. Work out the probability for each
result.
Working
Out of the six numbers (1, 2, 3, 4, 5, 6), the
number 4 only appears once.
What is the probability he will get a 4
on the white cube?
Thus:
1
6
2. What is the probability that he will There are three odd numbers out of the six
get an odd number on the red cube?
numbers (1, 2, 3, 4, 5, 6). Thus, there is a
probability that 3 out of 6 will be an odd
number.
Therefore:
3 !
=
6 !
©"SPECTRUM TUITION PTY LTD
160"
3. Multiply the two probabilities 1 1
×
since two events are occurring 6 2
concurrently.
!
= !"
Therefore, the answer is A
Question 16: C
Steps
1. Substitute x = 1 into the equation
Working
y = (x – 5)2 + 1
If x = 1, then:
y = (1 – 5)2 + 1
y = (– 4)2 + 1
y = 16 + 1
y = 17
Therefore the answer is C.
Question 17: A - y = −2x +4
Steps
1. Remember these coordinates are in
the form of (x, y).
(0, 4) means that when x = 0, y = 4
and (3, –2) means that when x = 3, y
= -2
2. Use trial and error and substitute
the known x values into the equations
to see if they match the y values.
Working
You will find that both options A & C will
satisfy (0,4), but only A will satisfy (3, -2).
Option A:
y = −2x +4
Substitute in x = 0
y = −2(0) +4
y=4
This is correct.
y = −2x +4 Substitute in x = 3
y = −2(3) +4
y = −6 +4
y = −2
This is correct
Option C:
y = 2x +4 Substitute in x = 0
y = 2(0) +4
y=4
This is correct
©"SPECTRUM TUITION PTY LTD
161"
y = 2x +4
Substitute in x = 3
y = 2(3) +4
y = 6 +4
y = 10
This is incorrect.
Thus the answer is A.
Question 18: C - - 7 and - 6
Steps
1. Factorise using the ‘cross method’
Working
x2 + 13x + 42 = 0
7 + 6 = 13
7 × 6 = 42
So 7 and 6 match what we need.
Thus, when we factorise:
2. Solve for x
Use the ‘Null factor law’
(x + 7)(x + 6) = 0
(x + 7)(x + 6) = 0
So:
(x + 7) = 0 or
(x + 6) = 0
Then:
(x + 7) = 0
x = -7 or
(x + 6) = 0
x = -6
Therefore the answer is C
Question 19: B - x > −6
Steps
Working
1. Solve the equation for x as normal 4 – 2x = 16
first 4 – 2x < 16
-2x = 16 – 4
x = -6
2. Now, because we used division x = -6
when working out the answer, we x > 16
need to flip the inequality sign given
in the question (change it from ‘less
than’ to ‘ greater than’)
Therefore the answer is B
©"SPECTRUM TUITION PTY LTD
162"
Question 20: A - $1259
Steps
Working
1. Let x be the unknown original
22
price.
× x = 277
Create an equation to express the 100
statement in the question.
22
2. Solve for x
100
× x = 277
277 × 100
=x
22
x = $1259.09
x = $1259 (round up)
Question 21: D - 24 3
Steps
Working
1. Use a tree diagram to break down
196 to its smallest factors (in red
circles).
2. Pair up numbers that are the same.
In this case, the 3 is the odd one out.
3. One of each paired number can
come out of the square root. So 192
can now be simplified as shown on
the right hand side.
192 = !2!×2×2 3! = 8 3
4. Multiply the simplified surd by 3 3×8 3 = 24 3
to answer the question.
Therefore the answer is D
©"SPECTRUM TUITION PTY LTD
163"
Question 22: B - 80
Steps
Working
1. Let x be the total number of people 40%!!"!! = 32"
who participated in this survey.
Create an equation to express the
statement in the question.
40
!×!! = 32"
100
40
!×!! = 32"
100
2. Solve for x
! = 32!×!
! =!
100
"
40
3200
40
! = !80"
Therefore, the answer is B
Question 23: C - 2 10
Steps
Working
1. Using Pythagoras’ theorem the ! ! = ! ! + ! ! "
length of b can be calculated.
!! = ! ! ! − ! !! "
Rearrange the theorem to find the
! = ! ! ! − ! !! "
length of b.
2. Substitute c = 7, and a = 3 into the ! = ! 7! − ! 3! "
equation to solve for b.
! = ! 49 − !9"
! = ! 40 = 2 10""
Therefore, the answer is C
Question 24: A - 2 39- 3
Steps
Working
1. In order to find the value of a, the ! ! = !! + ! ! "
length of the base of the bigger
!! = ! ! ! − ! ! ! "
triangle must be found.
! = ! ! ! − ! !!"
Let the length of the base = A
Using Pythagorean theorem
length of A can be calculated.
©"SPECTRUM TUITION PTY LTD
the
164"
2. Substitute c = 14, and b = 40 into
!
! = ! 14! − 40 "
the equation to solve for A.
! = ! 196 − !40"
! = ! 156""
3. Simplify the surd.
Since !! = ! + 3 ,
equation.
! = ! 156 = ! 2×2×3×13 = 2 39""
rearrange
this ! = ! + 3"
! = ! − 3"
Substitute ! = !2 39 into the new
! = 2 39 − 3!
equation to find a.
Therefore, the answer is A
Question 25: B - 78
Steps
Working
1. In order to find the length of GD, a !"! = !"! + !"!
series of Pythagoras’ theorem need to
be performed.
!" = ! !"! + ! !"!
Set
up
an
equation
using
Pythagorean theorem to find the
length of HD first.
2. Substitute CD = 2, and CH = 5 into !" = ! 2! + 5!
the equation to solve for HD.
!" = ! 4 + 25
!" = ! 29
3. Now that the length of HD is !"! = ! !"! + ! !"!
found, using the length of GH,
another equation can be set up to !" = ! !"! + ! !"!
determine the length of GD.
Substitute!GH! = !7, and !" = ! 29
into the equation to find GD
4.
Substitute !GH! = !7 ,
and
!
! + 29
!"
=
!
7
!" = ! 29 into the equation to find
GD
!" = ! 49 + 29 = ! 78
©"SPECTRUM TUITION PTY LTD
165"
Question 26: A – 15 cm
Steps
1. Let the length of each side of the
triangle to be x, y, and z. Since the
ratio of the lengths of 3 sides of the
triangle is 2:2:3, following equation
can be derived.
Working
!: !: ! = 2: 2: 3!
!
!
!
= ! = ! = !!!
2
2
3
Where k is a constant.
2. Rearrange above equation so that ! = !"
each length x, y, and z can be 2
expressed in terms of k.
! = 2!
!
=!
2
! = 2!
!
=!
3
! = 3!
3. Let P to be the perimeter of this ! = !! + ! + !"
triangle. Since perimeter of this
triangle is the sum of all 3 sides x, y,
and z, following equation can be set
up.
4. Substitute!!! = !35, ! = 2!,
! = 2!!!!"#!!! = 3! into the
equation to solve for k.
35 = !2! + 2! + 3!
35 = 7!
!=5
5. By comparing the ratio of each side ! = 3!
of the triangle, it can be determined
that z is the longest side of the ! = 3!×5 = 15!
triangle.
Therefore the answer is A
Substitute k =5 into z = 3k to find the
length of z.
©"SPECTRUM TUITION PTY LTD
166"
Question 27: B - 130
Steps
Working
1
1. Substitute the given values into the
! = ! ℎ(! + !)"
equation to find A.
2
1
! = ! !×20×(8 + 5)"
2
1
2. Using BODMAS, simplify the
bracket first, then move on to ! = ! 2 !×20×(13)"
multiplication to solve for A.
! = !10×13 = 130"
Therefore, the answer is B
!!
Question 28: A - !"
Steps
Working
1. Reduce both terms to a common 3! !
−! "
denominator (= the lowest common 5
4
multiple) between two denominators.)
!"#!!"#$""%!5!!"#!4!!"!20."
3!×4 !×5
−!
"
5×4
4×5
12! 5!
−! "
20
20
""
7!
2. Simplify the operation to find the 12! − 5!
=!
answer.
20
20
Therefore, the answer is A
©"SPECTRUM TUITION PTY LTD
167"
Question 29: A - y = (cz – ax) / b
Steps
1. Since y is to be the subject of the
equation and it is found on the left
hand side (LHS) of the equation,
remove other terms on the LHS by
moving them across the equation to
the right hand side (RHS).
Working
!" + !" = !""
!" = !!" − !""
"
When moving a term to the other side
of equation, the sign of the term
becomes opposite. In this case, the
sign of the term ax is positive on
LHS, but as it is moved to the RHS, it
becomes –ax.
!"
!" − !"
=!
!
!
2. Divide both sides by b.
! = !!
!" − !"
!
Therefore, the answer is A
Question 30: B - x > -4
Steps
1. First simplify the
expanding the bracket.
RHS
Working
by 25! − 10! > 5(4! − 6)"
25! − 10! > 20×! − 5×6"
25! − 10! > 20! − 30"
2. Rearrange the inequation such that
pronumeral x is on the LHS and the
rest is on the RHS.
25! − 20! > 10 − 30
3. Collect the like-terms, then divide 25! − 20! > 10 − 30
both sides by 5 to solve the
5! > ! −20
inequation.
5! −20
>
5
5
! > −4
Therefore the answer is B
©"SPECTRUM TUITION PTY LTD
168"
Question 31: A - 3 3 -14
Steps
1. Expand the bracket
Working
3 + 4 ×(2 3 − 5)"
= ! 3×2 3 + ! 3×−5 + 4×2 3 + 4×−5"
= 2!×3 − 5 3 + 8 3 − 20"
= 6 − 5 3 + 8 3 − 20"
2. Group the like-terms (i.e group = 6 − 20 + (8 3 − 5 3)
non-surds together and surds = ! −14 + 3 3!
together) and simplify them.
Therefore the answer is A.
Question 32: B
Steps
Working
1. Rearrange the equation into 2! − 3! = 4
! = !" + ! format, where m is the
gradient of the function and c is the y- 2! = 4 + 3!
intercept.
2! 4 3!
= +
2
2 2
!=
3!
+ 2!!"
2
3!
2. Find the x-intercept of the graph by
!=
+ 2!
letting y = 0.
2
0=
3!
+2
2
3!
= −2
2
2 3!
2
×
= ! −2×
3 2
3
4
3
3. Make a logical deduction based on The gradient of the function is positive and
information derived from the its x and y-intercept are at (− !, 0) and (0, 2)
!
equation to reach the answer.
respectively.
!=−
Since graph (a) and (d) have negative
gradients, they are ruled out of being the
©"SPECTRUM TUITION PTY LTD
169"
correct answer.
Although, both graph (b) and (c) have
positive gradients, graph (b) is the correct one
because its y-intercept is positive and its xintercept is negative whereas y-intercept of
graph (c) is negative and its x-intercept is
positive.
Therefore the answer is B.
Question 33: D
Steps
Working
1. In order to factorise this equation, 4 + (- 9) = - 5
you need to find 2 numbers that add
to make – 5 and multiply to make – 4x – 9 = - 36
36.
4 and - 9
2. Use these numbers to factorise the x2 – 5x – 36
= (x + 4)(x – 9)
equation.
Question 34: A - 1
Steps
Working
(y − y )
1. To find the gradient of a straight
m= 2 1
line, we use the following formula:
(x2 − x1 )
2. Plug in the values given to find the
value of m
(2, 1) (5, 4)
©"SPECTRUM TUITION PTY LTD
(4 − 1)
(5 − 2)
3
m=
3
m =1
m=
170"
Question 35: A -
( p − 3)
2
Steps
Working
1. Factorise the numerator by finding 4 and – 3
two numbers that add to make 1 and
Therefore, p2 + p – 12 = (p + 4)(p – 3)
multiply to make – 12.
2. Factorise the denominator by 2p + 8
taking out the common factor of 2.
= 2(p + 4)
3. Rewrite the equation with the
factorised
numerator
and
denominator.
p 2 + p −12
2p +8
( p + 4)( p − 3)
=
2( p + 4)
4. Cancel out the common factor of
( p + 4)( p − 3)
2( p + 4)
p−3
=
2
(p + 4)
Question 36: A -
g4
10
Steps
Working
1. Multiply the two values in the
f 9 × g4
denominator. When multiplying 2 f 5 × 5 f 4
indices, such as f5 and f4, add the
f 9 × g4
powers together.
=
10 f 9
2. Cancel out the f9 in both the
numerator and the denominator.
f 9 × g4
10 f 9
=
©"SPECTRUM TUITION PTY LTD
g4
10
171"
Question 37: D - 2n(m5)2 x n4
Steps
Working
1. Simplify A to see if it is correct. m 5n 3 × 2m 4 n 2
Remember, when you multiply like
9 5
indices, you add the powers and when = 2m n
you divide like indices, you subtract 2m 9 n 5 ≠ 2m10 n 5
the powers.
Not the right answer.
2. Simplify B to see if it is correct.
3. Simplify C to see if it is correct.
6m n4
3n
6m n3
=
3
m 3
6 n
≠ 2m10 n 5
3
Not the right answer.
(2m 5n 2 )2
= 2 2 m 5×2 n 2×2
= 4m10 n 4
4m10 n 4 ≠ 2m10 n 5
4. Simplify D to see if it is correct.
Not the right answer.
2n(m 5 )2 × n 4
= 2n(m 5×2 ) × n 4
= 2n(m10 ) × n 4
= 2n × m10 × n 4
= 2m10 n 5
5. Simplify E to see if it is correct.
This is the right answer.
2m 5
( 3 )2
n
2m 5×2
= 3×2
n
2m10
= 6
n
10
2m
≠ 2m10 n 5
n6
Not the right answer.
©"SPECTRUM TUITION PTY LTD
172"
Question 38: D - y = - 4x + 5
Steps
Working
1. Figure out what information about The gradient is clearly negative.
the gradient and the y-intercept we
The y-intercept is a positive value.
can identify from the graph.
Because the graph is not to scale, this is the
only information that we know. Don’t
assume that the y-intercept is 3 or the
gradient is -3/4.
2. All of the possible equations are
given in the form y = mx + c, where
m represents the gradient and c
represents the y-intercept. Identify the
equation that gives a positive y
intercept and a negative gradient.
y = - 4x + 5
Question 39: C – About 60
Steps
Working
1. Work out how many CDs could fit Width of CD = 14cm
within the width of the box.
Width of box = 28cm
28/14 = 2
2. Work out how many CDs should Length of CD = 12.5 cm
fit within the length of the box.
Length of box = 38 cm
38/12.5 = 3 remainder 0.5cm
Approximately 3.
3. Work out how many CDs would fit Height of CD = 1 cm
within the height of the box.
Height of box = 10 cm
10/1= 1
4. Multiply these 3 values together to 2 x 3 x 10 = 60
find the approximate number of CDs
that will fit in the box.
©"SPECTRUM TUITION PTY LTD
173"
Question 40: B - 4 10cm
Steps
1. The radius of the circle is the third
shortest side of a right angled triangle
with a hypotenuse of 22 cm. Use
Pythagoras’ theorem to find the
missing side.
Working
c2 = a2 + b2
a = the radius of the circle
b = 18cm
c =22cm
222 = a2 + 182
2. Solve for a to find the radius.
222 = a2 + 182
a2 = 222 – 182
a2 = 484 – 324
a2 = 160
a = 160
3. Simplify the surd.
a = 160
a = 16×10
a = 16× 10
a = 4 10
Question 41: A - t =
8
Cos25°
Steps
Working
1. Figure out which trigonometric
Adjacent
ratio is most appropriate for this Cosθ = Hypotenuse
situation.
2. Substitute the known values into
8
Cos25° =
the equation.
t
3. Rearrange the equation to solve for
t.
©"SPECTRUM TUITION PTY LTD
t=
8
Cos25°
174"
Question 42: C - x =
17
tan 60 o
Steps
Working
1. Determine which of the trigonometric
O
tan
θ
=
ratios is required; that is, SOH-CAHA
TOA
2. Substitute the given values into the
17
tan 60 o =
ratio
x
o
3. Transpose the equation and solve for x tan 60 = 17
x
17
x=
tan 60 o
Question 43: B - 6
Steps
Working
1. Cancel out any common factors 5 42 × 4 6
between the numerator and the
10 28
denominator.
42 × 4 6
=
2 28
=
42 × 2 6
28
=
3×2 6
2
=
3×2 3
1
= 3×2 3
2. Multiply these values together.
= 3×2 3
= 2 3× 3
=2 9
= 2×3
=6
©"SPECTRUM TUITION PTY LTD
175"
Question 44: B - 2ay(2a - 5y)
Steps
Working
1. In order to factorise, start by 4!! ! − 10!! !
identifying the highest common
!"# = 2!"
factor between two terms.
2. Take out the HCF and place it
outside the bracket as shown.
4!! ! 10!! !
2!"
−
2!"
2!"
2!"(2! − 5!)!
Therefore the answer is B.
Question 45: C - (-3, 0)
Steps
Working
1. To find the point of intersection, x 2 + 4x + 3 = 2x + 6
make the two functions equal one
another.
2. Solve for x to find the x coordinate x 2 + 4x + 3 = 2x + 6
of the intercept. There may be 2
2
values of x, which suggest that there x + 4x − 2x + 3 − 6 = 0
are 2 intercepts.
x 2 + 2x − 3 = 0
(x − 1)(x + 3)
either
x −1 = 0
x =1
or
x+3= 0
x = −3
3. Substitute the values of x back in to When x = 1
one of the equations to find the values y = 2(1) + 6
of y.
y =2+6
y=8
When x = -3
y = 2(−3) + 6
y = −6 + 6
y=0
4. State the coordinates of the The graphs intercept at (1, 8) and (-3, 0). The
intersection.
only answer which gives on of these points is
C.
©"SPECTRUM TUITION PTY LTD
176"
Question 46: C
Steps
1. Expand the brackets.
Working
− 5(3 10 − 2 20 )
= −3 50 + 2 100
= 2 100 − 3 50
2. Simplify the irrational numbers.
2 100 − 3 50
= 2(10) − 3 25 2
= 20 − (3 × 5) 2
= 20 − 15 2
Question 47: E
Steps
Working
1. Multiply the numerator and the
4
5 +1
×
denominator by 5 +1 . Due to the
5 −1
5 +1
difference of two squares rule, this
4( 5 +1)
will cause the denominator to become
=
rational.
( 5 −1)( 5 +1)
2. Use the difference of two squares
rule to simplify the denominator and
cancel out the common factor of 4.
=
4( 5 + 1)
( 5 )2 − 12
4( 5 + 1)
5 −1
4( 5 + 1)
=
4
= 5 +1
=
©"SPECTRUM TUITION PTY LTD
177"
Question 48: E -
d
4( 2 d + 9)
Steps
Working
1. To divide fractions, simply invert d − 4 (d − 4)(2d + 9)
÷
the second fraction and multiply.
20
5d
d−4
5d
×
20
(d − 4)(2d + 9)
5d(d − 4)
=
20(d − 4)(2d + 9)
=
2. Simplify by cancelling out the
common factors of (d-4) and 4.
Question 49: D - 106
5d(d − 4)
20(d − 4)(2d + 9)
5d
=
20(2d + 9)
d
=
4(2d + 9)
2
Steps
Working
1. To simplify the equation, change
128 = ! 64×2 = 8! ×2 = 8 2
the surds into the smallest surds
possible.
−2 72 = −2 36×2 = −2 6! ×2
= −2×6 2 = ! −12 2
11 200 = 11 2×100 = 11 2×10!
= 11×10 2 = 110 2
2. Since all the surds are alike, simply 8 2 − 12 2 + 110 2 = 106 2
complete the question by collecting
them.
Therefore the answer is D
©"SPECTRUM TUITION PTY LTD
178"
Question 50: B - 2x – 5
Steps
Working
1. Factorise the numerator by taking 6! − 15 3 2! − 5
=
out the HCF.
3
3
2. Cancel out the common factor
between
the
numerator
and
denominator.
! !!!!
!
= 2! − 5
Therefore the answer is B
Question 51: B -
5x + 8
(2 x − 1)( x + 1)(3x + 2)
Steps
Working =
3
2
1. Reduce two fractions to the
−
common denominator (=LCM)
2! − 1 ! + 1
! + 1 3! + 2
The LCM is: (2! − 1)(! + 1)(3! + 2)
3
3! + 2
×
2! − 1 ! + 1 3! + 2
=
3 3! + 2
2! − 1 ! + 1 3! + 2
−
2
2! − 1
×
! + 1 3! + 2 2! − 1
=−
2. Now that two fractions have the
same denominator, the original
equation can be written as shown.
3. Expand the brackets on top and
simplify by collecting the like-terms.
2 2! − 1
2! − 1 ! + 1 3! + 2
! !!!! !! !!!!
!!!! !!! !!!!
!
=
9! + 6 − 4! + 2
2! − 1 ! + 1 3! + 2
=
5! + 8
!
2! − 1 ! + 1 3! + 2
Therefore the answer is B
©"SPECTRUM TUITION PTY LTD
179"
Question 52: E - 4.9 sin 26o
Steps
Working
!""!#$%&
1. Figure out which trigonometric
sin ! =
ratio is most appropriate for this
!"#$%&'&()
situation.
2. Substitute the known values into sin 26° = !
!.!
the equation.
! = 4.9 sin 26°
3. Rearrange the equation to solve for
x.
Therefore the answer is E.
Question 53: D - 2 y + 15
12
Steps
Working
1. Reduce the two fractions to the 3! + 7 4! − 1
−
lowest
common
multiple
6
12
denominator. The LCM between 6
and 12 is 12, so convert the = 3! + 7 × 2 − 4! − 1
6
2
12
denominator of the first fraction to 12
by multiplying top and bottom by 2.
2 3! + 7
4! − 1
=
−
12
12
2. Now that two fractions have the
same denominator, the original
equation can be written as shown.
=
! !!!! ! !!!!
!"
6! + 14 − 4! + 1
3. Expand the brackets on top and
=
simplify by collecting the like-terms.
12
=
2! + 15
12
Therefore the answer is D.
Question 54: D – 23
Steps
1. Let two numbers to be x and y
where x is greater than y. Using the
information, following equations can
be set up.
Working
The greater of 2 numbers is 7 more than the lesser
number: ! = ! + 7
Three times the greater number is 5 more than 4
times the lesser number: 3! = 4! + 5
2. Solve it simultaneously by using Substitute ! = ! + 7 into 3! = 4! + 5
substitution method.
3 ! + 7 = 4! + 5
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3! + 21 = 4! + 5
4! − 3! = 21 − 5
! = 16
The lesser number is 16, so substitute this
back into ! = ! + 7
! = 16 + 7 = 23
Therefore the greater number is 23 and hence
D is the answer.
Question 55: B - ( 2 1 , − 5 )
2
Steps
Working
1. To determine the intersection Using substitution method:
between two functions, we solve the
Substitute ! = 4! − 15 into!2! + ! = 0.
two equations simultaneously.
2! + 4! − 15 = 0
6! − 15 = 0
6! = 15
!=
15 5
=
6
2
2. To find the corresponding y Substitute ! = !" into ! = 4! − 15
!
coordinate of the intersection,
!"
substitute ! = ! into any of the
5
! = 4×
− 15
original equation.
2
20
!=
− 15
2
! = !!10 − 15 = ! −5
Therefore the point of intersection is at
!
(! , −5)!!and hence the answer is B.
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Question 56: A - ! = −5
Steps
1. To solve for x, start by rearranging
the equation so that all x terms are on
the left hand side and non-x terms are
on the right hand side.
Working
! 3 2!
− =
5 7
7
2. Multiply both sides by 35 to get rid
of fractions.
35×
! 2! 3
−
=
5 7
7
!
−
!
!!
!
!
= ! ×35
35! 70! 105
−
=
5
7
7
7! − 10! = 15
3. Simplify the left hand side by 7! − 10! = 15
collecting the like-terms.
−3! = 15
4. Divide both sides by -3 to find the −3! 15
=
value of x.
−3
−3
! = −5
Question 57: D - L1: y = −x + 5
L2: y = −x – 4
Steps
1. By looking at the graph, it can be
deduced that two linear equations
share the same gradient but differ in
their y-intercepts as two equations are
parallel to each other.
Working
Rule out any option where two linear
equations have different gradients.
Option B and C are ruled out.
2. Since two equations demonstrate Option A is ruled out.
negative gradients, any option with
positive gradient is ruled out.
3. This leaves us with option D and E Option D:
as viable answers. Check whether
! = ! −! + 5
option D represents the graph.
! = −! − 4
Option D has two linear equations that each
has a negative gradient and x- and yintercepts of (5, 0) and (0, 5), and (-4, 0) and,
(0, -4) respectively. These features are
observed in the graph so the answer is D.
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Question 58: B - 3a !
Steps
Working
1. To simplify the surd, take out the
9!! ! = ! 3! !! ! = 3! !
base of any squared number or
pronumeral and place it in front of the Therefore the answer is B.
square root sign.
Question 59: C - $139,500
Steps
Working
1. Let x = the selling price of the Mr. Salinas, a real estate agent, received a 5%
house
commission on the selling price of a house:
5%!!"!! = $6975
!
2. Change ‘of’ to multiplication sign
!×! = $6975
!""
and 5% to its equivalent fraction, then
solve for x.
100 5!
100
×
= $6975×
5
100
5
! = $1395×100 = $139,500
Therefore the answer is C.
Question 60: A - y + 4
Steps
Working
1. Factorise the top using the !! − ! ! = (! + !)(! − !)
difference of square rule.
! ! − 16 = ! ! − 4! = ! + 4 ! − 4 !
2. Rewrite the equation incorporating
the factorized numerator.
(! ! !!")
(!!!)
=
(!!!)(!!!)
!!!
3. Cancel out common factor between (! + 4)(! − 4)
= !! + 4!
top and bottom to reach the answer.
!−4
Therefore the answer is A
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
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READING COMPREHENSION
EXAM PAPER 3
Detailed Solutions
Question 1: D
"I am sure he said to himself, 'Watch me make them scamper,'" she said. Earhart, who
felt a mixture of fear and pleasure, stood her ground.
The contrast is made between the choice to “scamper” and the choice she made to
“stand her ground”. The opposite of standing one’s ground is fleeing.
Question 2: D
Amelia was 10 in 1907, meaning she was born in 1897. Thus, in 1920, when she first
rode in a plane, she must have been 23.
Question 3: B
The first paragraph indicates that “It wasn't until Earhart attended a stunt-flying
exhibition, almost a decade later, that she became seriously interested in aviation”
Question 4: C
Amelia’s attitude to flying was initially unimpressed (“It was a thing of rusty wire and
wood and looked not at all interesting”), but shifted to passionate (“By the time I had
got two or three hundred feet off the ground," she said, "I knew I had to fly.")
Question 5: D
Option A: Given that Amelia was born in 1897, and died in 1937, it might be inferred
that Amelia was 40, not 39, when she died. However, the passage indicates that when
she made her fateful flight she was “nearing her 40th birthday”.
Option B: The islands she was travelling to are mentioned to be in the Pacific
Option C: “They flew into overcast skies and intermittent rain showers”
Option D is the only false statement given, as Fred Noonan was Earhart’s navigator,
not co-pilot.
Question 6: A
The author’s tone is factual, as the events are relayed with little emotion.
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Question 7: C
Options A, B and D are too literal: the proverbs message is broader than simply a
lesson about metals. Option C is correct: all that glitters (or appears attractive) is not
gold (or may be deceiving you).
Question 8: A
The intended audience of this piece can be inferred from a number of facts:
•
•
•
The title of the publication, The Cook’s Oracle and Housekeeper’s Manual,
indicates it is to instruct prospective cooks
The first sentence states “On your first coming into a family”, referencing the
arrival of a cook to a new family
Servants are referred to as “your fellow servants”, implying the reader is one
too. This is supported by the reference to the family as “your employers”
Question 9: A
Option B: “Take care to be on good terms with the servant who waits at table”
Option C: “Judge of your employers from YOUR OWN observations,
and THEIR behaviour to you, not from any idle reports from the other servants”
Option D: “Beware of believing such honey-tongued folks”
Option A is the only piece of advice not given: the first paragraph states that the cook
should get to know how the kitchen and house operate “on your first coming into a
family”, not before arriving.
Question 10: C
Option A: There is nothing in the passage to suggest the reader must obey every
command given
Option B: The reader is warned to “be most cautious of those who profess most”,
suggesting that they should not make close relationships with everyone
Option D: This is incorrect, as the reader is advised to “lose no time in immediately
getting into the good graces of your fellow-servants”
Option C is correct, as the focus of the second half of the passage is on making sure
the reader uses her instincts to decide who is trustworthy and who is not; in addition,
the value of asking questions is indicated in the advice to “make use of him (the
waiter) as your sentinel, to inform you how your work has pleased in the parlour”.
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Question 11: C
The metaphor “honey tongued” creates an image of a person whose tongue is coated
with honey (or sweet/kind words) but who is really concerned with their own
interests.
Question 12: C
We can infer that orders were given to turn the lights out after dark because, as the
camp is on the war front, enemy planes would look for lights as targets to bomb.
Question 13: D
The horses were attempting to “embark” the boat at the beginning of its journey. The
author notes this was difficult to do. Both of these facts suggest they were boarding,
or getting on, the boat.
Question 14: A
Option A is correct, given the descriptions used (“great send off”, “an exciting scene”,
“quite so thrilling”, “waved and yelled”)
Question 15: A
A flashback is a reference to the past within a text: the author does this as she begins
in the present (with the order given), refers to the past (the send off), and then reverts
back to the present (snatching up the supper). The other options do not describe this
technique: a simile is a comparison between two things using like or as;
personification is giving non human things human qualities; foreshadowing is giving
clues to the reader as to events that will occur later in the text.
Question 16: B
Option A: “snatch up a very scratch supper and turn in, only rugs and blankets”
Option C: “our start off from Ireland”
Option D: The diarist does not complain about the orders given, nor the basic
conditions, suggesting that she has adapted to her situation.
Option B is the only fact not supported by the text: the diarist refers to “All the 600
khaki men on board”, but as she is a nurse we can infer there were other people on the
boat besides officers.
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Question 17: D
The diarist is more resigned than in Excerpt 1. She does not appear confident (Option
A), enthusiastic (Option B) or frustrated (Option C): rather, she is accepting of her
circumstances, and reveals information with little emotion (“One of the last lot of
officers told us he had himself seen in a barn three women and some children, all
dead, and all with no hands”). She is accepting, and weary, of her circumstances, an
attitude best described as resigned (Option D).
Question 18: D
The diarist has experienced the horrors of war (“One of the last lot of officers told us
he had himself seen in a barn three women and some children, all dead, and all with
no hands”), become used to the conditions (“there was nothing doing, lay down in our
clothes and slept”) and contributed to the war effort (“We were all so tired and done
up yesterday” suggests she has been working hard.)
Question 19: C
The banging noise indicates they are losing the war, rather than winning (Option A);
the impression we get of the nurse is of someone kindy and compassionate, so the
suggestion she misses the noise because it means more people will be injured (and
thus she will have more work), does not seem likely (Option B) and there is nothing
to suggest she is being sarcastic (Option D). Rather, in line with her resigned,
accepting attitude, it seems most likely she misses the noise because it is a constant
presence in her life and she has become used to it.
Question 20: A
Describing something as being ‘legendary’ indicates that Jack often solves problems
well. We can therefore eliminate B and C. It is not an agreement therefore, the only
answer that makes sense is A.
Question 21: E
“I usually spent my summers at my cousins’ large, spacious and impressive house”
Option E is the only option to contain:
•
•
•
•
A capital “I” at the beginning of the sentence
An apostrophe in “cousins’” to indicate the house belongs to his multiple
cousins
A comma after “large” to indicate items are being listed
A full stop at the end of the sentence
Note that, as in Option A, “cousin’s” could also be correct (as we have no way of
knowing how many cousins the author has.) However, there are other errors in Option
A.
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Question 22: C
Fire is a good servant (can serve man well) but a bad master (should not be allowed to
control man).
Question 23: B
The word “slight” is used in reference to the density of the planets: the “slighter” of
the two, Saturn, would float in water, which suggests slightness is a reference to small
size.
Question 24: A
Option B: “still very hot within—although but slightly, if at all, incandescent at the
surface—and, therefore, unsuited to contain life”
Option C: “Saturn's immense distance from the sun will always prevent it from
receiving an amount of solar radiation consistent with our ideas of what is required by
a living world”
Option D: As for Option C
Option A is correct: Saturn’s density is “slight”, one eighth of earth’s, but the pull of
gravity is about the same: “If the relative weight of bodies on the surfaces of planets
formed the sole test of their habitability, Venus and Saturn would both rank with the
earth as suitable abodes for men”
Question 25: C
Option C is correct, as ““If the relative weight of bodies on the surfaces of planets
formed the sole test of their habitability, Venus and Saturn would both rank with the
earth as suitable abodes for men”
Question 26: B
The author would agree that it is impossible to live on other planets (“always prevent
it from receiving an amount…”) but is clearly interested in the possibility, as he has
dedicated a substantial passage to the idea. Thus, Option A is incorrect, but Option B
is correct. Options C and D are not supported by the text, as the author acknowledges
the impossibility of living on other planets.
Question 27: D
Options B and C are too literal. Option A is the opposite of the intended meaning: a
dog that barks (a person who makes threats) seldom bites (or rarely carries through
with the action)
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Question 28: A
“You and I were the only ones to go to Matt’s house”
Option A is the only option that contains:
•
•
The verb “were” to refer to “You and I” (as “You and I” are plural, they
require a plural verb)
The verb “to go” in the present tense (“went” in Option D is a past tense verb,
which does not match the original sentence)
Question 29: B
The sentence is in the past tense (“lost”) and, thus, the replacement sentence must also
be in the past tense. Option B is the only option with the correct tense.
Question 30: B
The word “hence” in the original sentence means “thus” or “as a result” – it implies a
result. Option B maintains this meaning by suggesting that my sister wants to become
a model because she is photogenic. Option A implies a result (that she wants to
become a model and therefore she is photogenic); Option C suggests that she wants to
become a model even though she is photogenic (not because) and Option D is in the
past tense, rather than the present tense as is the original sentence.
Question 31: A
Alice is obviously young and is proving herself as self-sufficient, but cannot yet be
described as that yet.
Question 32: E
The mother does not really expect Alice to keep herself busy so when she sees Alice
has even cleaned up after herself, she will likely be proud.
Question 33: D
The little voice is most likely Alice’s conscience because it is telling Alice to do right
and is not an actual voice, but thoughts. The narrator is telling the story, Alice’s sister
is not there, Peggy Morinda is a doll, and it is clear Alice is not insane.
Question 34: B
“I know,” said Jack: “it will be fun!” is the line that shows Jack came up with the
idea.
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Question 35: E
Lines 15 and 16 have Jack explaining what the children will use as skates and how to
attach them to their feet.
Question 36: E
The poem explains that Jack got right back up and began skating again after his fall.
He was not injured.
Question 37: E
The term expansive means large or sizeable, so sizeable would be the correct option.
Question 38: B
While both superb and exacting can serve as synonyms for the term exquisite,
someone would want a dress to look superb before wanting the dress to appear
exacting. Option B makes the most sense.
Question 39: B
The term ‘managed retreats’ implies an involvement by government. Option B is the
best example of this.
Question 40: C
Option C is the best answer as it encompasses all of the ways in which the use of
fossil fuels increased so rapidly.
•
•
•
Option A, although a fact, does not explain how the shift was responsible for
the increase in greenhouse gases
Option B had already been taking place for hundreds of years
Option D did not occur until decades later
Question 41: C
An ecosystem is a group of interdependent organisms living in an environment that
they inhabit and depend on. Option A is the only word with a similar meaning.
Question 42: D
Options A, B & C do not acknowledge that in spite of official indifference or
negativity, people are usually either educated or interested enough to form their own
opinions. Option D refers mainly to third world countries where education is not
compulsory or affordable.
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Question 43: B
Wilson believes the interviewer is asking for his opinion as a scientist, so this is how
he answers. Option B reflects this point of view.
Question 44: C
•
•
•
Option A: There are no penguins in the Arctic, the home of seals and polar
bears
Option B: Glaciers are retreating, rather than changing course
Option D: This is unlikely at the present time
Question 45: D
•
•
Options A and C: These consequences are not mentioned in the extract
Option B: It is the land, rather than the crops, which is becoming heavily
salted
Question 46: B
•
•
•
Option A: Helen was not able to imitate her mother’s action as she could not
see them
Option B: Almost correct, but it does not mention Helen’s dependence on her
mother
Option D: the implication is that either Helen was able to see what her mother
was doing or that she was separate from her mother
Question 47: B
•
•
•
Option A: There was no electricity in the house
Option C: Helen’s parents were able to afford a helper to look after her, so
they were not poor
Option D: Although the passage describes Helen’s mother as cooking, this
was part of the everyday housework rather than a paid occupation
Question 48: D
The sentence describes what Helen believes she can remember, so the term ‘I fancy’
is closest in meaning to ‘I believe’. Her memories are confused because she was very
ill and very young.
Question 49: D
•
•
•
Option A: Helen was not able to imitate her mother’s action as she could not
see them
Option B is incorrect. For example, in Southern India, tilting the head at an
angle to each side can say 'I'm not sure'
There is no evidence for Option C in the extract
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Question 50: A
Options A, B and C are good pointers to Helen’s intelligence but the phrase ‘set my
spirit free’ indicates there was more to come.
END OF SOLUTIONS.
REATTEMPT ANY QUESTIONS YOU ANSWERED INCORRECTLY UNTIL
YOU ANSWER IT CORRECTLY.
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