SAT
1.
(1+1)÷ 1 =
5 3
2
(A)
1
8
(B)
1
4
(1+1)÷ 1 =
5 3
2
4
(C)
15
(D)
1
2
(E)
16
15
(E)
16
15
3+5 ÷ 1 =
15
2
8 • 2 = 16
15 1
15
SAT
2.
x 2 – 2 x when x = – 2 ?
(A) – 8
(B) – 4
(C)
0
(D)
4
(E)
8
(E) 8
x 2 – 2 x when x = – 2 ?
(– 2 ) 2 – 2 (– 2 ) =
4+4=8
SAT
3.
Kate read 96 pages in 2 hours and 40 minutes.
What was Kate’s average rate of pages per hour?
(A) 24
(B) 30
(C) 36
(D) 42
(E)
48
(C) 36
x = 96
60 160
x = 96 • 60
160
x = 6 • 60
10
x = 6 • 6 = 36
SAT
4.
For how many integer values of x will 7/8 be greater than ¼ and less than 1/3 ?
(A) 6
(B) 7
(C) 12
(D) 28
(E)
Infinite many
1 > 7 > 1
3 x
4
( 1 > 7 > 1 ) 12 x
3 x
4
4 x > 84 > 3 x
_______________________________________________________________________________________
4 (22) > 84 > 3 (22) --- 88 > 84 > 66
(A) 6
4 (23) > 84 > 3 (23) --- 92 > 84 > 69
4 (24) > 84 > 3 (24) --- 96 > 84 > 72
4 (25) > 84 > 3 (25) --- 100 > 84 > 75
4 (26) > 84 > 3 (26) --- 104 > 84 > 78
4 (27) > 84 > 3 (27) --- 108 > 84 > 81
SAT
5.
What is the average (arithmetic mean) of 2 x + 5, 5 x – 6 , – 4 x + 2 ?
(A)
x+1
3
(B) x + 1
(C)
3x+1
3
2x+5
5x–6
–4x+2
3x+1
(D) 3 x + 3
(E)
3x+31
3
(A)
x+1
3
3x+1= x+1
3
3
SAT
7.
In this triangle, what is the degree measure of angle B ?
A
(A) 45
70⁰
(B) 60
(C) 65
(D) 75
(E)
80
C
45⁰
B
< B + < C + < A = 180⁰
(C) 65⁰
< B + 45⁰ + 70⁰ = 180⁰
< B + 115⁰ = 180⁰
< B = 180⁰ – 115⁰ = 65⁰
SAT
8.
For all x ≠ 0, x2 + x2 + x2 =
x2
(A) 3
(B) 3 x
(C) x2
(D) x3
(E)
x4
(A) 3
x2 + x2 + x 2 =
x2
3 x2 = 3
x2
SAT
8.
For all x ≠ 0, x2 + x2 + x2 =
x2
(A) 3
(B) 3 x
(C) x2
(D) x3
(E)
x4
(A) 3
x2 + x2 + x 2 =
x2
3 x2 = 3
x2
SAT
9.
The equation x2 = 5x – 4 has how many distinct real solutions ?
(A) 0
(B) 1
(C) 2
(D) 3
(E)
Infinitely many
(C) 2
x2 = 5 x – 4
x2 – 5 x + 4 = 0
(x–4)(x–1)=0
x = 4 or 1
SAT
Which of the following sets of numbers has the property that the sum of any two
10. numbers in the set is also a number in the set ?
I. The set of even integers
II. The set of odd integers
III. The set of prime numbers
(A) I only
1+3=4
Ex where odd integers doesn’t work
(C) I and II only
3+5=8
Ex where prime doesn’t work
(D) I and III only
2+4=6
Even Integers does work
(B) III only
(E)
I, II, and III
(A) I only
SAT
Bob’s average (arithmetic mean) score after 4 tests is 89. What score on the 5th
11. test would bring Bob’s average up to exactly 90?
(A) 90
(B) 91
(C) 92
89 x 4 = 356
90 x 5 = 450
(D) 93
(E)
94
(F) 94
So, the difference between the 2 gives
us the total needed to average 90
450 – 356 = 94
SAT
The price s of a sweater is reduced by 25% for a sale. After the sale, the reduced
12. price is increased by 20%. Which of the following represents the final priceo f the
sweater ?
(A) 1.05 s
(B) .95 s
(C) .90 s
(D) .85 s
(E)
Sale price is 25 % off or .75 s
Post sale price is increased by 20 %
The increase = .75 s x .2 = .15 s
.80 s
Then we add .75 s + .15 s = 90 s
(C)
.90 s
SAT
13.
How many distinct prime factors does the number 36 have ?
(A) 2
(B) 3
(C) 4
(D) 5
(E)
6
(A) 2
36
2 x 18
2x3x6
2x3x2x3
SAT
15.
If the area of a triangle is 36 and its base is 9, what is the length of the altitude to
that base?
(A) 2
(B) 4
(C) 6
(D) 8
(E)
12
(D) 8
AT = 1 hb = 36
2
1 h (9) = 36
2
h (9) = 36
2
h = 36 • 2
9
h=8
SAT
Let a  be defined for all positive integers a by the equation a  = a – a
15. If x  = 3, what is the value of x ?
4 6
(A) 18
(B) 28
(C) 36
(D) 40
(E)
54
(C) 36
If a  = a – a
4 6
x= x –x
4 6
If x  = 3
 3 = x –x
4 6
12 (3 = x – x )
4 6
36 = 3 x – 2 x
36 = x
SAT
16.
Betty has q quarters, d dimes, n nickels and no other coins in her pocket. Which of
the following represents the total number of coins in Joan’s pocket ?
(A) q + d + n
(B) 5q + 2d + n
(C) .25q + .10d + .05n
(D) (25 + 10 + 5) (q + d + n )
(E)
25q + 10d + 5n
(A) q + d + n
This is a “TRAP” question:
The problem only asks for the total
# of coins, NOT the total value of
coins, which is what you are lead to
think.
SAT
17. Which of the following is an equation for the graph above ?
(A) y = –2 x + 1
(B) y = x + 1
•
(C) y = x + 2
(D) y = 2 x + 1
(E)
y=2x+2
•
(E) y = 2 x + 2
The slope is 2 and the y-intercept is 2,
so the answer is y = 2 x + 2
SAT
If an integer is divisible by 6 and 9, then the integer must be divisible by which of
18. the following ?
I. 12
II. 18
III. 36
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E)
I, II, and III
Prime factors of 6 are 2 x 3, so any # divisible should
have at least one 2 and one 3 as factors
Prime factors of 9 are 3 x 3, so any # divisible should
have at least two 3’s as factors

Any # divisible by both should have at least one 2
and two 3’s and the first possibility is 2 x 32 or 18
12 and 36 require two 2’s in its prime factorization
(B) II only

12 doesn’t have a 2nd prime factor of 3
36 does work in some cases by NOT all, such as the
most obvious one, 6 x 9 or 54.
SAT
19.
In this figure, O is the center of the circle and P, O, and Q are collinear. If < ROQ
measures 50⁰, what is the degree measure of <RPQ ?
(A) 20
(B) 25
(C) 30
(D) 35
(E)
40
(B) 25
P
?
O
Q
50⁰
R
< POR =180⁰ – 50 ⁰ = 130 ⁰
PO = OR (all radii are =)
< RPQ = <PRO (base <‘s of Isosceles are =)
and < QPR + <PRO = 50 ⁰  < RPQ =25
SAT
A wooden cube with volume 64 is sliced in half horizontally,. The two halves are
20. then glued together to form a rectangle solid which is not a cube. What is the
surface area of this new solid?
(A) 128
2
(B) 112
(C) 96
64
2
(D) 56
(E)
48
E3 = 4 x 4 x 4 = 64
4
(B) 112
4
2
4
E3 = 4 x 4 x 4 = 64
Two rectangle solids 4 x 4 x 2, when glued 2 x 4 x 8
Then Top and Bottom = 8 x 4 = 32 or 64 total
Then Front and Back = 8 x 2 = 16 or 32 total
Then two sides = 4 x 2 = 8 or 16 total
4
4
Grand total of 6 sides
= 64 + 32 + 16 = 112
SAT
A drawer contains 6 blue socks, 12 black socks and 15 white socks. If one sock is
21. chosen at random, what is the probability that it will be black?
(A)
1
4
(B)
1
3
(C)
3
8
(D)
1
2
(E)
5
8
(C)
6 blue
12 black
15 white
32 Total
Black 12 = 3
Total 32 8
3
8
SAT
Danielle drives from here home to the store at an average speed of 40 miles per
22. hour. She returns home along the same route at an average speed of 60 miles per
hour. What is her average speed, in miles per hour, for her entire trip ?
(A) 45
(B) 48
(C) 50
(D) 52
(E)
55
(A) 48
This is a TRAP question ! We are NOT given enough
information to use a distance formula. So we need to
improvise by selecting a distance that is easy to work with.
Since we have speeds of 40 and 60 mph, why not use a
multiple of both, such as, 120
Distance = rate x time
(going trip)
120 = 40 t where t = 3 hours
(return trip)
120 = 60 t where t = 2 hours
Now 240 = 5 r, where r = 48 miles per hour
SAT
23.
What is the area of a right triangle if the length of one leg is a and the length of
the hypotenuse is c ?
(A)
ac
2
c2 = a2 + b2
ac – a2
(B)
2
a3 + c3
(C)
2
(D) a
(E)
c2– a2
2
a2 + c2
(D)
c2 – a2 = b2
c2
a2
√ c 2 – a2 = b
AT = ½ h b
b2
A = 1 a ( √ c 2 – a2 )
2
SAT
24.
In ∆ PRS, RT is the altitude to side PS and QS is the altitude to side PR. If RT = 7,
PR – 8 and QS = 9, what is the length of PS ?
(A)
5 1
7
(B)
6 2
9
(C)
7 7
8
(D)
10 2
7
(E)
13 4
9
R
Q
P
T
S
AT = ½ h b
Using altitude QS and side PR = ½ • 9 • 8 = 36
10 2
(D)
7
Using altitude RT with side PS = ½ • 7 • PS = 36
7 PS = 36 then, PS = 36 • 2 = 10 2
2
7
7
SAT
There are 3 routes from River City to Bayville.
25. There are 4 routes from Bayville to Eagles Mere.
There are 3 routes from Eagles Mere to Twin Peaks.
If a driver must pass through Bayville, and Eagles Mere exactly once, how many
possible ways are there to go from River City to Twin Peaks.
(A) 6
(B) 10
(C) 12
(D) 24
(E)
36
(E) 36
River City
1 2 3
[3]
x
Bayville
1 2 3 4 [4]
x
Eagles Mere
1 2 3
[3]
=
Twin Peaks [ 36 ]