SHSAT MATH PRACTICE TEST WITH ANSWERS

(1)  Five apples and 6 bananas together cost as much as 8 bananas and 9 pears.  One apple costs as much as 2 pears.  For the same price as 1 pear, how many bananas could be bought?

(A)  1  (B)  2  (C)  3  (D)  4  (E)  6

Solution

(2)  Let R = 8 · 9 · 7 · 13 and S = 4 · 6 · 11 · 49.  The greatest common factor of R and S is

(A)  12  (B)  42  (C)  56  (D)  168  (E)  504

Solution

(3)  What is the value of 4|x – y| - 3|xy| if x = -5 and y = 2?

(A)  -42  (B)  -18  (C)  -2  (D)  42  (E)  58

Solution

(4)  In the following sequence of eight numbers, each number has one more “1” than the number before it:

2, 12, 112, 1112,. . . . , 11111112

What is the hundreds digit in the sum of all eight of these numbers?

(A)  0  (B)  6  (C)  7  (D)  8  (E)  9

Solution

(5)  In Ms. Hsiao’s class there are twice as many boys as there are girls.  Half of the boys are in the math club and all of the girls are in the math club.  What percent of Ms. Hsiao’s class is in the math club?

(A)  25%  (B)  33  (1/3)%  (C)  50%

(D)  66 (2/3)%  (E)  75%

Solution

(6)  (16 + 5x) – (8 – 2x) =

(A)  8 + 3x  (B)  8 - 3x (C)  8 - 7x

(D)  8 + 7x (E)  24 - 7x

Solution

(7)  The three lines shown intersect in a point.  The value of x

(A)  is 100.  (B)  is 80.  (C)  is 50.  (D)  is 20. 

(E)  cannot be determined from the given information

Solution

(8)  The straight line graph shows how many people are in a large cafeteria eating lunch at different times.  If the people leave at a steady rate, at what time will oly 150 people remain?

(A)  1:15 P.M.  (B)  1:30 P.M.  (C)  1:45 P.M. 

(D)  2:15 P.M.  (E)  3:30 P.M.

Solution

(9)  Two congruent circles have centers P and Q as shown.  What is the measure of angle PXQ?

(A)  30°  (B)  45°  (C)  55°  (D)  60°  (E)  75°

Solution

(10)  Andrew has d dollars.  He has one-third as many dollars as Bruce has.  Carlos has $80 less than half the total of Andrew’s and Bruce’s dollars.  In terms of d, how many dollars does Carlos have?

(A)  4d – 40  (B)  2d – 40  (C)  2d + 40 

(D)  2d + 80  (E)  2d – 80

Solution

(11)  The sum of 7 unequal positive integers is 61.  What is the largest possible value that any of those integers can have?

(A)  55  (B)  40  (C)  39  (D)  13  (E)  9

Solution

(12)  In the set {1, 5, x, 10, 15}, the integer x is the median.  The mean of the five numbers is one less than x.  The value of x is

(A)  6  (B)  7  (C)  8  (D)  9  (E)  none of these.

Solution

(13)  If 7/50 < 1/x < 8/51 where x is an integer, then x =

(A)  8  (B)  7  (C)  6  (D)  5  (E)  4

Solution

(14)  Half of 2⁸ is

(A)  2⁷ (B)  2⁶ (C)  2⁴ (D)  1⁸  (E)  8

Solution

(15)  If x is greater than 1/2 but less than 1, which of the following has the largest value?

(A)  2x – 1  (B)  x²  (C)  1/x  (D)  1 – x  (E)  x³ 

Solution

(16)  Maria, Anoki, and Boris are teenagers, and the sum of their ages now is 49.  The sum of their ages 8 years from now will be F, and the sum of their ages 10 years ago was P.  The value of F – P is

(A)  54  (B)  18  (C)  17  (D)  6  (E)  2

Solution

(17)  If (1/4) + (1/x) = 1, then x =

(A)  1/8  (B)  2/3  (C)  4/3  (D)  2  (E)  3

Solution

(18)  When the integer N is divided by 7,  the quotient is Q and the remainder is 5.  When N + 24 is divided by 7, the remainder is ‘

(A)  4  (B)  3  (C)  2  (D)  1  (E)  0

Solution

(19)  Point B is on line segment AD, and point E is on line segment BC.  The value of x is

(A)  20  (B)  40  (C)  50  (D)  60  (E)  70

Solution

(20)  Three-fourths of a number is equal to L.  What is three-halves of that original number, in terms of L?

(A)  4/3L  (B)  3/2L  (C)  2L  (D)  3L  (E)  4L

Solution