SASMO Primarv 3
1
Dhision
Sinppore and Asian
P3
Schools Math Olympiad
2015
Full Name:
Index Number:
Class:
School:
INSTRUCTIONS
1. Please DO NOT OPEN the contest booklet until the Proctor has given permission.
2. TIME: 1 hour 30 minutes.
3. Attempt all 20 questions.
Questions 1 to 10 score 2 points each, no points are deducted for unanswered question
and 1 point is deducted for wrong answer.
Questions 11 to 20 score 4 points each. No points are deducted for unanswered or
wrong answers.
4. Shade your answers neatly using a pencil in the answer sheet.
5. PROCTORING: No one may help any student in any way during the contest.
6. No electronic devices capable of storing and displaying visual information is
allowed during the course of the exam.
7. Strictly No calculators are allowed into the exam.
8. All students must fill and shade in in their Name, Index number, Class and School in
the answer sheet and contest booklet.
9. MINIMUM TIME: Students must stay in the exam hall at least 1h 15 min.
10. Students must show detailed working and transfer answers to the answer sheet.
11. No exam papers and written notes can be taken out by any contestant.
11
2
Rough Working
12
3
SASMO 2015, Primary 3 Contest
SASMO 2015 PRIMARY 3 [10 MCQ + 10 non-MCQ"' 20 Q]
Starting Score = 10 marks (to c1void negative marks); Max Possible Score = 70 marks
section A (Correct answer
1.
2.
!!!!!
2 marks; no answer
=O; incorrect an§w@r =minu§ 1 mark)
Find the missing term in the following sequence: 1, 2, 4, 7, _ _, 16.
(a)
10
(b)
11
(c)
12
(d)
13
(e)
14
2s means 2 multiplied by itself 5 times, i.e. 2 5
34 equal to?
(a)
7
(b)
12
(c)
27
(d)
81
(e)
None of the above
13
4
=2x
2
x
2
x
2
x
2
= 32. What is
SASMO 2015, Primary 3 Contest
3.
An operator
3
o
acts on two numbers to give the following outcomes:
o 2 = 51
5 o 3 = 82
6 O 1 = 75
9
I)
What is 7
4.
4
I)
= 135
5 equal to?
(a)
112
(b)
121
(c)
122
(d)
212
(e)
None of the above
The diagram shows a figure that contains 7 identical squares. The area of the
figure is 112 cm 2 • Find its perimeter.
(a)
56 cm
(b)
60 cm
(c)
64 cm
(d)
68 cm
(e)
72 cm
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SASMO 2015, Primary 3 Contest
5.
6.
FIii tn the blank: _ _ _ _ Is 4 tens 5 ones greater than 2 tens 7 ones.
(a)
18
(b)
28
(c)
62
(d)
72
(e)
None of the above
Which of the following statement(s) is or are correct?
Statement A: 7 + (0 x 2) = 7
Statement B: 7 + (0 -a- 2) = 7
Statement C: 7 + (2 x O) = 7
(a)
All the three statements are correct.
(b)
Only Statements A and Bare correct.
( c)
Only Statements A and C are correct.
( d)
Only Statements B and C are correct.
(e)
None of the above
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SASMO 2015, Primary 3 Contest
7.
There are 4 types of cakes available In a cake shop: chocolate, cheese, blueberry
and blackforest. Naomi wants to buy 2 different types of cakes. How many
different choices does sh@ have?
8.
(a)
4
(b)
6
(c)
8
(d)
10
(e)
12
Find the total number of squares in a 3 x 3 square grid.
(a)
9
(b)
10
(c)
13
(d)
14
(e)
15
16
7
SASMO 2015, Primary 3 Contest
9.
Find the smallest whole number between 14 and 40 that Is divisible by 3 and
by 4.
10.
(a)
12
(b)
16
(c)
18
(d)
24
(e)
36
What is the length of the largest square that can be made from 50 onecentimetre square tiles?
(a)
5 cm
(b)
6 cm
(c)
7cm
(d)
8 cm
(e)
None of the above
17
8
SASMO 2015, Primary 3 Contest
section B {Correct answer = 4 marks; Incorrect or no an5wer = 0)
11.
Two numbers are such that
• the first number is greater than or equal to 5, but less than or equal to 8
• the second number is greater than or equal to 2, but less than or equal to
10.
Find the least possible value of the sum of the two numbers.
12.
If the four-digit number 12N4 is divisible by 3 and N is less than 5, find N.
18
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SASMO 2015, Primary 3 Contest
13.
A whole number multiplied by itself will give a special type of numbers called
perfect squares. Examples of perfect squares are 9 (~ 3
What is the smallest number that can be multiplied
Find the day of the week that is 50 days from a Monday.
19
10
3) and 16 (= 4
x
4).
by 2.8 to give a perfect
square?
14.
x
SASMO 2015, Primary 3 Contest
15.
Amy wants to cut rectangular cards of length 4 cm by 3 cm from a rectangular
sheet 32 cm by 21 cm. Find the biggest number of cards that can be cut from
the sheet.
16.
There are 5 items (a ruler, a pen, an eraser, a sharpener and a hole puncher)
lying in a straight row on a table. The eraser is next to the hole puncher and the
sharpener. The ruler is next to the hole puncher. The sharpener is the first item
on the left. What is the order of the items on the table from left to right?
20
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SASMO 2015, Primary 3 Contest
17.
In the following, all the different letters stand for different digits. Find the twodigit NO.
N
18.
O
N
A
N
N
0
50 cakes are packed in two different box sizes. The small box holds 4 cakes and
the big box holds 6 cakes. If less than 10 boxes are used and all the boxes are
fully packed, how many big boxes are used?
21
12
SASMO 2015, Primary 3 Contest
19.
Allee and Ben are sister and brother. Alice has as many sisters as she has
brothers, but Ben has twice as many sisters as he has brothers. How many boys
and girls are there in their family?
20.
The diagram shows a rectangle being divided into 3 smaller rectangles and a
square. If the perimeter of the unshaded rectangle is 16 cm and the area of the
square is 9 cm 2, find the total area of the shaded rectangles.
End of Paper
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SASMO 2015, Primary 3 Contest
Solutions to SASMO 2015 Primary 3
Section A
1.
Find the missing term in the following sequence: 1, 2, 4, 7, _ _ 16.
(a)
{b)
(c)
(d)
(e)
10
11 [Ans: 7 + 4]
12
13
14
Solution
The pattern is as follows:
1,
2,
4,
7,
, 16
\..__;11 \..__;11 \..__;11 \..__;11 \..__;11
+2
+3
25 means 2 multiplied by itself 5 times, i.e. 25 = 2 x 2 x 2 x 2 x 2 = 32. What is
34 equal to?
(a)
7
(b)
(c)
27
nd
2.
+s
yl
in
: . the missing term is 7 + 4 = 11.
+4
e
+1
12
(d) 81 [Ans]
None of the above
tre
(e)
Solution
34
3.
=3 X
3
X
3
X
3
= 81
An operator ¢ acts on two numbers to give the following outcomes:
3
¢
5
¢
6
¢
9
¢
= 51
3 = 82
1 = 75
4 = 135
2
What is 7 ¢ 5 equal to?
(a)
(b)
(c)
(d)
112
121
122 [Ans]
212
(e)
None of the above
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SASMO 2015, Primary 3 Contest
Solution
o b = (a+ b)(a - b)
:. 7 ¢ 5 = 122
iJ
(a)
(b)
{c}
(d)
(e)
56 cm
60 cm
64 cm [Ans]
68 cm
72 cm
Solution
e
The diagram shows a figure that contains 7 identical squares. The area of the
figure is 112 cm 2 • Find its perimeter.
yl
in
4.
Area of 7 identical squares = 112 cm 2
nd
Area of one square= 16 cm 2
Length of square = 4 cm
tre
Since the perimeter of the figure is made up of 16 sides of a square, then its
perimeter
= 16 x length of square
= 16 X 4
= 64cm
5.
Fill in the blank: _ _ __
(a)
(b)
(c)
{d}
( e)
is 4 tens 5 ones greater than 2 tens 7 ones.
18
28
62
72 [Ans]
None of the above
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SASMO 2015, Primary 3 Contest
Solution
4 tens 5 ones greater than 2 tens 7 ones is 45 + 27
= 72.
: . the missing number is 72
6.
Which of the following statement(s) is or are correct?
Statement A: 7
+ (0 x 2) = 7
Statement B: 7 + (0 + 2) = 7
Statement C: 7 + (2 x 0) = 7
e
All the three statements are correct. [Ans]
Only Statements A and Bare correct.
Only Statements A and Care correct.
Only Statements B and C are correct.
None of the above
yl
in
(a)
(b)
(c)
( d)
(e)
Solution
Statement A: 7 + (0 x 2) = 7 + O = 7
Statement B: 7
+ (0 _,_ 2) = 7 + 0 = 7
nd
Statement C: 7 + (2 x 0) = 7 + O = 7
.-. all the three statements are correct.
There are 4 types of cakes available in a cake shop: chocolate, cheese, blueberry
and blackforest. Naomi wants to buy 2 different types of cakes. How many
different choices does she have?
(a)
(b)
(c)
(d)
(e)
tre
7.
4
6 [Ans]
8
10
12
Solution
Method 1 (Systematic Listing)
Chocolate
Cheese
Blueberry
Blackforest
./
./
./
./
./
./
./
./
./
./
:. total no. of choices= 6
25
16
./
./
SASMO 2015, Primary 3 Contest
Method 2 (Rephrase the Problem)
Choosing 2 types of cakes from 4 types is the same as the handshake problem of
4 people shaking hands once with one another.
.-. total no. of choices = 3 + 2 + 1
=6
Find the total number of squares in a 3 x 3 square grid.
9
10
13
14 [Ans]
e
(a)
(b)
(c)
(d}
(e)
yl
in
8.
15
Solution
+ 4 + 1 = 14
Find the smallest whole number between 14 and 40 that is divisible by 3 and by
4.
tre
9.
nd
No. of 1 x 1 squares = 9
No. of 2 x 2 squares = 4
No. of 3 x 3 squares = 1
: . total no. of squares in a 3 x 3 square grid = 9
(a)
(b)
(c)
(d}
(e)
12
16
18
24 [Ans]
36
Solution
Method 1
Numbers between 14 and 40 that are divisible by 4 are:16, 20, 24, 28,32 and 36.
Of these 6 numbers, only 24 and 36 are divisible by 3.
:. the smallest whole number between 14 and 40 that is divisible by 3 and by 4
is 24.
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SASMO 2015, Primary 3 Contest
Note: A number that is between 14 and 40 does not Include 14 and 40. If we
start with numbers divisible by 3, there will be more possibilities.
Method 2
A number that is exactly divisible by both 3 and 4 must also be exactly divisible
by 12.
The only numbers between 14 and 40 that are exactly divisible by 12 are 24 and
36.
: . the smallest whole number between 14 and 40 that is divisible by 3 and by 4
is 24.
(e)
5 cm
6 cm
7 cm [Ans]
8 cm
None of the above
Solution
nd
(a)
(b)
(c)
(d)
yl
in
e
What is the length of the largest square that can be made from 50 onecentimetre square tiles?
Since 7 x 7 = 49 and 8 x 8 = 64, then the length of the largest square that can
be made from 50 one-centimetre square tiles is 7 cm.
tre
10.
27
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SASMO 2015, Primary 3 Contest
Section B
11.
Two numbers are surh that
• the first number is greater than or equal to 5, but less than or equal to 8
• the second number is greater than or equal to 2, but less than or equal to
10.
Find the least possible value of the sum of the two numbers.
Solution
Least possible value of the sum of the two numbers
= least possible value of first number + least possible value of second number
=5+2
If the four-digit number 12N4 is divisible by 3 and N is less than 5, find N.
Solution
yl
in
12.
e
=7
Using the divisibility test for 3, 1 + 2 + N + 4 = N + 7 is also divisible by 3.
nd
Since N is a single digit, N = 2, 5 and 8.
But N is less than 5 (given).
13.
=2
tre
:. N
A whole number multiplied by itself will give a special type of numbers called
perfect squares. Examples of perfect squares are 9 ( = 3 x 3) and 16 ( = 4 x 4).
What is the smallest number that can be multiplied by 28 to give a perfect
square?
Solution
Since 28 = 2 x 2 x 7 = (2 x 7) x 2, then the smallest number that can be
multiplied by 28 to give a perfect square is 7, so that (2 x 7) x (2 x 7) = 14 x 14
is a perfect square.
28
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SASMO 2015, Primary 3 Contest
14.
Find the day of the week that is
so days from a Monday.
Solution
By counting, 7 days from a Monday is Monday.
So 49 days(= 7 x 7 day) from a Monday is still Monday.
: . SO days from a Monday is Tuesday.
e
Amy wants to cut rectangular cards of length 4 cm by 3 cm from a rectangular
sheet 32 cm by 21 cm. Find the biggest number of cards that can be cut from
the sheet.
yl
in
Solution
32 cm + 4 cm = 8 cards along the length of the rectangular sheet.
21 cm + 3 cm = 7 cards along the breadth of the rectangular sheet.
nd
.-. biggest number of cards that can be cut from the sheet= 8 x 7 = 56
tre
15.
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SASMO 2015, Primary 3 Contest
16.
There are 5 items (a ruler, a pen, an eraser, a sharpener and a hole puncher)
lying in a straight row on a table. The eraser is next to the hole puncher and the
sharpener. The ruler is next to the hole puncher. The sharpener is the first item
on the left. What is the order of the items on the table from left to right?
Solution
The sharpener is the first item on the left.
s , _ _, ____, __
The eraser is next to the hole puncher and the sharpener.
I
H
E
yl
in
s
e
This means that the eraser is the second item next to the sharpener, and the
hole puncher is the third item.
The ruler is next to the hole puncher.
S ,
H ,
E
R
17.
tre
nd
Thus the last item is the pen .
.-. the order of the items on the table from first to last is sharpener, eraser,
hole puncher, ruler and pencil.
In the following, all the different letters stand for different digits. Find the twodigit NO.
N
O
N
A N
N
0
Solution
In the ones column, N - N = 0, so O = 0.
In the hundreds column, if N ~ 2, the final answer for the subtraction will be a 3digit number, so N = 1.
Now NO - A= N implies that 10 - A= 1, so A= 9 .
.-. NO
= 101 -
91
= 10.
30
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SASMO 2015, Primary 3 Contest
18.
so cakes are packed in two different box sizes. The small box holds 4 cakes and
the big box holds 6 cakes. If less than 10 boxes are used and all the boxes are
fully packed, how many big boxes are used?
SOiution
Since the question states that 'less than 10 boxes are used', it suggests that
there should be more big boxes than small boxes. So we use guess and check
starting with fewer small boxes:
No. of Cakes
Left
so - 4 = 46
so - 8 = 42
50 - 12 = 38
so - 16 = 34
so - 20 = 30
1
2
3
4
5
No. of Big Boxes
46
+
Total No. of
Boxes
6 has left over
42 + 6 = 7
38 + 6 has left over
34 + 6 has left over
30 + 6 = 5
e
No. of Small
Boxes
9
10
: . no. of big boxes used
Solution
nd
Alice and Ben are sister and brother. Alice has as many sisters as she has
brothers, but Ben has twice as many sisters as he has brothers. How many boys
and how many girls are there in their family?
tre
19.
=7
yl
in
Note: Actually you can stop after getting a total of 9 boxes because if you use
more small boxes, the total no. of boxes will be bigger than 9.
Method 1 (Guess and Check)
Since Alice is a girl and she has as many sisters as she has brothers, then the
number of girls in the family is one more than the number of boys.
Ben has twice as many sisters as he has brothers.
True or false?
2 girls and 1 boy
Ben has 2 sisters and O brother. Above statement is false.
3 girls and 2 boys
Ben has 3 sisters and 1 brother. Above statement is false.
4 girls and 3 boys
Ben has 4 sisters and 2 brothers. Above statement is
true.
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SASMO 2015, Primary 3 Contest
Using guess and check as shown in the above table, there are 3 boys and 4
girls in the family.
Method 2 (Model Method}
For Alice
Boys
Girls
1
''
''
'''
For Ben
Boys
I
1
''
''
'
''
'
'
e
I
yl
in
Girls
From the model for Ben, 1 unit for Girls
= 1 + 1 = 2.
:. there are 3 boys and 4 girls in the family.
nd
The diagram shows a rectangle being divided into 3 smaller rectangles and a
square. If the perimeter of the unshaded rectangle is 16 cm and the area of the
square is 9 cm 2, find the total area of the shaded rectangles.
tre
20.
Solution
Put the two shaded rectangles to form a long rectangle as shown:
Length of long rectangle = .!. x perimeter of unshaded rectangle
2
= -21 x
16 cm
= 8 cm
Breadth of long rectangle = length of square = 3 cm
:. total area of shaded rectangles = 8 cm x 3 cm = 24 cm 2
32
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