SAT problem solving practice test 01
1. Of the following, which is greater than ½ ?
A. 2/5
B. 4/7
C. 4/9
D. 5/11
E. 6/13
2. If an object travels at five feet per second, how many feet does it travel in one hour?
A. 30
B. 300
C. 720
D. 1800
E. 18000
3. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190
inclusive?
A. 90
B. 95
C. 100
D. 105
E. 110
4. A cubical block of metal weighs 6 pounds. How much will another cube of the same
metal weigh if its sides are twice as long?
A. 48
B. 32
C. 24
D. 18
E. 12
5. In a class of 78 students 41 are taking French, 22 are taking German. Of the students
taking French or German, 9 are taking both courses. How many students are not enrolled
in either course?
A. 6

B. 15
C. 24
D. 33
E. 54
6. If f(x) = │(x² – 50)│, what is the value of f(-5) ?
A. 75
B. 25
C. 0
D. -25
E. -75
7. ( √2 - √3 )² =
A. 5 - 2√6
B. 5 - √6
C. 1 - 2√6
D. 1 - √2
E. 1
8. 2
30
+ 2
30
+ 2
30
+ 2
30
=
A. 8
120

B. 8
30


C. 2
32

D. 2
30

E. 2
26

9. Amy has to visit towns B and C in any order. The roads connecting these towns with
her home are shown on the diagram. How many different routes can she take starting
from A and returning to A, going through both B and C (but not more than once through
each) and not travelling any road twice on the same trip?
A. 10
B. 8
C. 6
D. 4
E. 2
10. In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?
A. 18
B. 13.5
C. 9
D. 4.5
E. 3
SAT problem solving practice test 02
1. Which of the following could be a value of x, in the diagram above?
A. 10
B. 20
C. 40

D. 50
E. any of the above
2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes
per hour, or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large
cakes and 700 small cakes are needed. How many helpers are required?
A. 10
B. 15
C. 20
D. 25
E. 30
3. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian
stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US
to British stamps?
A. 5 : 1
B. 10 : 5
C. 15 : 2
D. 20 : 2
E. 25 : 2
4. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
5. Two sets of 4 consecutive positive integers have exactly one integer in common. The
sum of the integers in the set with greater numbers is how much greater than the sum of
the integers in the other set?
A. 4
B. 7
C. 8

D. 12
E. it cannot be determined from the information given.
6. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the
greatest value?
A. f(-1)
B. f(0)
C. f(1)
D. f(3)
E. f(4)
7. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC
respectively. What is the area of the quadrilateral EBFD ?
A. 2.25
B. 3
C. 4
D. 4.5
E. 6
8. If n ≠ 0, which of the following must be greater than n?
I 2n
II n²
III 2 - n
A. I only
B. II only
C. I and II only
D. II and III only
E. None
9. After being dropped a certain ball always bounces back to 2/5 of the height of its
previous bounce. After the first bounce it reaches a height of 125 inches. How high (in
inches) will it reach after its fourth bounce?
A. 20
B. 15

C. 8
D. 5
E. 3.2
10. n and p are integers greater than 1
5n is the square of a number
75np is the cube of a number.
The smallest value for n + p is
A. 14
B. 18
C. 20
D. 30
E. 50
1. The distance from town A to town B is five miles. C is six miles from B. Which of the
following could be the distance from A to C?
I 11
II 1
III 7
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, or III.
2. √5 percent of 5√5 =
A. 0.05
B. 0.25
C. 0.5
D. 2.5
E. 25
3. If pqr = 1 , rst = 0 , and spr = 0, which of the following must be zero?
A. P

B. Q
C. R
D. S
E. T
4.
A. 1/5
B. 6/5
C. 6³
D. 6
4
/ 5
E. 6
4

5. -20 , -16 , -12 , -8
In the sequence above, each term after the first is 4 greater than the preceding term.
Which of the following could not be a term in the sequence?
A. 0
B. 200
C. 440
D. 668
E. 762
6. If f(x) = x² – 3, where x is an integer, which of the following could be a value of f(x)?
I 6
II 0
III -6
A. I only
B. I and II only
C. II and III only
D. I and III only

E. I, II and III
7. For how many integer values of n will the value of the expression 4n + 7 be an integer
greater than 1 and less than 200?
A. 48
B. 49
C. 50
D. 51
E. 52
8. In the above correctly worked addition sum, A,B,C and D represent different digits,
and all the digits in the sum are different. What is the sum of A,B,C and D?
A. 23
B. 22
C. 18
D. 16
E. 14
9. 12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm
breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm
3
)
A. 6
B. 8
C. 10
D. 20
E. 40
10. Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how
old is Ben now in terms of P ?
A. 11/P + 6
B. P/11 +6
C. 17 - P/6

D. 17/P
E. 11.5P
1. If a² = 12, then a
4
=
A. 144
B. 72
C. 36
D. 24
E. 16
2. If n is even, which of the following cannot be odd?
I n + 3
II 3n
III n² - 1
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
3. One side of a triangle has length 8 and a second side has length 5. Which of the
following could be the area of the triangle?
I 24
II 20
III 5
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
4. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues

to eat at the same rate, in how many more days will its total consumption be 91 pounds?
A. 12
B. 11
C. 10
D. 9
E. 8
5. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125
are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily
be a perfect cube?
A. 8p
B. pq
C. pq + 27
D. -p
E. (p - q)
6

6. What is the length of the line segment in the x-y plane with end points at (-2,-2) and
(2,3)?
A. 3
B. √31
C. √41
D. 7
E. 9
7. n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 6, 10, 14, 18}
What is the probability that n + p = 23 ?
A. 0.1
B. 0.2

C. 0.25
D. 0.3
E. 0.4
8. A dress on sale in a shop is marked at $D. During the discount sale its price is reduced
by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff
member buys the dress what will she have to pay in terms of D ?
A. 0.75D
B. 0.76D
C. 0.765D
D. 0.775D
E. 0.805D
9. All the dots in the array are 2 units apart vertically and horizontally. What is the length
of the longest line segment that can be drawn joining any two points in the array without
passing through any other point ?
A. 2
B. 2√2
C. 3
D. √10
E. √20
10. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100,
what is the best approximation to the length of arc AB ?
A. 9
B. 10
C. 11
D. 12
E. 13
1. Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day
on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324
per week. How much does she earn in dollars per hour?
A. 11

B. 10
C. 9
D. 8
E. 7
2. ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is
the perimeter of the parallelogram?
A. 12
B. 9√3
C. 9
D. 8
E. 3√3
3. If the product of 6 integers is negative, at most how many of the integers can be
negative?
A. 2
B. 3
C. 4
D. 5
E. 6
4. If a positive integer n, divided by 5 has a remainder 2, which of the following must be
true?
I n is odd
II n + 1 cannot be a prime number
III (n + 2) divided by 7 has remainder 2
A. none
B. I only
C. I and II only
D. II and III only
E. I, II and III
5. A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2.
How many of the smaller cubes have paint on exactly 2 sides?

A. 30
B. 24
C. 12
D. 8
E. 6
6. Line l contains the points (3,1) and (4,4).
If line m is a different line, parallel to line l in the same coordinate plane, which of the
following could be the equation of line m?
A. y = 3x - 8
B. y = 1/3x - 3
C. y = -3x - 8
D. y = 3x + 1
E. y = -8x + 3
7. In the figure above the square has two sides which are tangent to the circle. If the area
of the circle is 4a²π, what is the area of the square?
A. 2a²
B. 4a
C. 4a²
D. 16a²
E. 64a²
8. A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and
x + 1. Which of the following could be the length of the other side?
A. 2
B. 4
C. 6
D. 8
E. 10
9. A machine puts c caps on bottles in m minutes. How many hours will it take to put
caps on b bottles?
A. 60bm/c

B. bm/60c
C. bc/60m
D. 60b/cm
E. b/60cm
10. Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has
by mistake added water so that he has 6 litres of paint which is half water and half paint.
What must he add to make the proportions of the mixture correct?
A. 1 litre paint
B. 1 litre water
C. ½ litre water and one litre paint
D. ½ litre paint and one litre water
E. ½ litre paint
1. Which of the following can be used to illustrate that not all prime numbers are odd?
A. 1
B. 2
C. 3
D. 4
E. 5
2. What is the greatest of 3 consecutive integers whose sum is 24 ?
A. 6
B. 7
C. 8
D. 9
E. 10
3. Considering the positions on the number line above, which of the following could be a
value for x?
A. 5/3
B. 3/5
C. -2/5
D. -5/2

E. none
4. A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for
each. What is the maximum number of bows that can be made?
A. 8
B. 9
C. 10
D. 11
E. 12
5. How many numbers between 200 and 400 meet one or both of the conditions given in
the two statements below?
Statement 1: The number begins with 3
Statement 2: The number ends with 3
A. 20
B. 60
C. 100
D. 110
E. 120
6. If f(3) = 15 and f(5) = 45, which of the following could be f(x)?
A. 4x + 3
B. 2x² – 2x
C. 2x² - x
D. 2x² - 5
E. 5x²
7. PQRS is a parallelogram and ST = TR. What is the ratio of the area of triangle QST to
the area of the parallelogram?
A. 1 : 2
B. 1 : 3
C. 1 : 4
D. 1 : 5
E. it cannot be determined

8. A picture is copied onto a sheet of paper 8.5 inches by 10 inches. A 1.5 inch margin is
left all around. What area in square inches does the picture cover?
A. 76
B. 65
C. 59.5
D. 49
E. 38.5
9. The table shows the results of a poll which asked drivers how many accidents they had
had over the previous 5 years. What is the median number of accidents per driver?
A. 0.5
B. 1
C. 1.5
D. 2
E. 4
10. If V = 12R / (r + R) , then R =
A. Vr / (12 - V)
B. Vr + V /12
C. Vr - 12
D. V / r - 12
E. V (r + 1) /12
1. The number 0.127 is how much greater than 1/8 ?
A. ½
B. 2/10
C. 1/50
D. 1/500
E. 2/500
2. Which of the following could not be the lengths of the sides of a right angled triangle?
A. 3, 4, 5
B. 5, 12, 13
C. 8, 15, 17

D. 12, 15, 18
E. 9, 12, 15
3. Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles
have the maximum diameter possible. What is the approximate area of the paper
remaining after the circles have been cut out?
A. 104
B. 78
C. 54
D. 27
E. 13
4. If a and b are both positive, which of the following is a simplification of the expression
above?
A. a² + b² + 1
B. a + b
C. a - b
D. ab
E. it cannot be simplified further
5. x = y - (50/y), where x and y are both > 0
If the value of y is doubled in the equation above, the value of x will
A. decrease
B. stay the same
C. increase four fold
D. double
E. increase to more than double
6. Which of the following could be a solution of the equation │x│ = │4x - 3│
A. -1
B. -0.6
C. 0
D. 0.6
E. 1.5

7. The number of degrees that the hour hand of a clock moves through between noon and
2.30 in the afternoon of the same day is
A. 720
B. 180
C. 75
D. 65
E. 60
8. Jeff takes 20 minutes to jog around the race course one time, and 25 minutes to jog
around a second time. What is his average speed in miles per hour for the whole jog if the
course is 3 miles long?
A. 6
B. 8
C. 10
D. 12
E. 14
9. A and B are equidistant from the line l. How many circles can be drawn with their
centres on line l and that pass through both A and B?
A. 1
B. 2
C. 3
D. 4
E. >10
10. A wheel has a diameter of x inches and a second wheel has a diameter of y inches.
The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does
the second wheel make in covering d feet?
A. 100xy
B. 100y - x
C. 100x - y
D. 100y / x
E. 100x / y

1. 3x + y = 19 , and x + 3y = 1.
Find the value of 2x + 2y
A. 20
B. 18
C. 11
D. 10
E. 5
2. The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20
per cent. The two reductions together are equal to a single reduction of
A. 45%
B. 40%
C. 35%
D. 32.5%
E. 30%
3. x and y are integers
x + y < 11 , and x > 6
What is the smallest possible value of x - y ?
A. 1
B. 2
C. 4
D. -2
E. -4
4. If x
5
y
4
z
2
<0 , which of the following must be true?
I xy <0

II yz <0
III xz <0
A. I
B. II
C. III
D. I and II
E. None
5. BCD is a line segment and Angle BAC = ¼ Angle ACB ; Angle ACD = ?
A. 140
B. 100
C. 120
D. 60
E. it cannot be determined from the information given
6. Which of the following integers is in the solution set of │1 – 3x│ < 5 ?
I -1
II 1
III 2
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
7. In a certain village, m litres of water are required per household per month. At this
rate, if there are n households in the village, how long (in months) will p litres of water
last?
A. p /mn
B. mn / p
C. mp / n
D. np / m
E. npm

8. In the figure below, what is the slope of line l ?
A. - 3
B. - 1/3
C. 0
D. 1/3
E. 3
9. What digit appears in the units place in the number obtained when 2
320
is multiplied
out?
A. 0
B. 2
C. 4
D. 6
E. 8
10. Radius of circle center O is 3 times the radius of circle center C.
Angle ACB = Angle POQ
If the shaded area of circle C is 2 then what is the area of the shaded part of circle O ?
A. 6
B. 12
C. 18
D. 36
E. 3/2
1. (3 x 10
4
) + (2 x 10²) + (4 x 10) =
A. 302400
B. 32400
C. 30240
D. 3240

E. 324
2. Andy solves problems 74 to 125 inclusive in a Math exercise. How many problems
does he solve?
A. 53
B. 52
C. 51
D. 50
E. 49