SHSAT PRACTICE TEST MATH

(1)  If 3x + 2y  =  19 and 2x + 3y  =  91, what is the value of x + y ?

(A)  8  (B)  9  (C)   21  (D)  22  (E)  72

Solution

(2)  Kenny buys candy bars at 9 for $1 and sells them at 3 for $1. How many candy bars must he sell in order for his to make a profit of exactly $10.

(A)  27  (B)  30  (C) 45  (D)  60  (E)  90

Solution

(3)  Juan travels at the rate of 30 miles per hour for 4 hours. He then returns over the same route in  hours. What was his average rate for the return trip, in mile per hour ?

(A)  22  1/2  (B)  34  2/7  (C)  35  (D)  36  (E)  40

Solution

(4)  The value of 3⁵ + 3⁵ + 3⁵ is 

(A)  3⁶  (B)  3¹⁵  (C)  9⁵  (D)  9¹²⁵  (E)  4⁵

Solution

(5)  Lindsay has P dollars and mark has $9 less than Lindsay. If mark receives an additional $11, how many dollars will mark now have, in terms of P?

(A)  P - 20  (B)  20 - P  (C)  P + 2  (D)  2 - P  (E)  P +  11

Solution

(6)  R = 2 ⋅ 3 ⋅ 3 ⋅ 5 ⋅ 7 ⋅ 11 ⋅ 11 and S = 3 ⋅ 7 ⋅ 13 ⋅ 17, what is the greatest common factor of Rand S?

(A)  2 ⋅ 3 ⋅ 3  ⋅ 3 ⋅ 5 ⋅ 7  ⋅ 7 ⋅ 11 ⋅ 11  ⋅ 13  ⋅ 17

(B)  2 ⋅ 3 ⋅ 3 ⋅ 5 ⋅ 7  ⋅ 11  ⋅ 13  ⋅ 17

(C)   3 ⋅ 7  (D)  3 ⋅ 3 ⋅ 7 ⋅ 7  (D)  3 ⋅ 3 ⋅ 3 ⋅ 7 ⋅ 7

Solution

(7)  The counting numbers are placed in order in the chart, as shown. Assuming the pattern continues, in which column will the 200 appear ?

(A)  Q  (B)  S  (C)  T  (D)  U  (E)  V

Solution

(8)  The equation 2(3x + 6)  =  3(2x + 4) is satisfied by 

(A)  No value of x  (B)  Only negative values of x 

(C)  Only x = 0 

(D)  only positive values of x  (E)  all values of x

Solution

(9)  Wai ling averaged 84 on her first three exams and 82 on her next 2 exams. What grade must she obtain on her sixth test in order to average 85 for all six exams. 

(A)  96  (B)  94  (C)  90  (D)  89  (E)  86

Solution

(10)  How many prime numbers between 8 and 60 leave a remainder of 2 when divided by 6 ?

(A)  0  (B)  1  (C)  4  (D)  6  (E)  7

Solution

(11)  In a diagram, each small box is a square whose side is 3. What is the area of the shaded figure ?

(A)  108  (B)  54  (C)  36  (D)  18  (E)  6

Solution

(12) When expressed in scientific notation, the number 1, 230, 000, 000 is 1.23 x 10^B. The value of B is 

(A)  2  (B)  7  (C)  8  (D)  9  (E)  10

Solution

(13)  In a diagram, lines m and n are parallel. What is the value of x ?

(A)  20  (B)  40  (C)  45  (D)  60  (E)  70

Solution

(14)  If p =  √(2 + √10), Q  =  √(10 + √2) and R = √(5 + √5)

(A)  P < Q < R   (B)  P < R < Q  (C)  Q < R < P 

(D)  R < Q < P  (E)  P  =  Q

Solution

(15)  The sides of a triangle all have integer lengths. Two side have lengths 7 and 10. If the largest and smallest possible perimeters for the triangle are L and S, the value of L + S.

(A)  is 20  (B)  is 51  (C) is 52 (D)  is 54 

(E)  cannot be determined from the information given

Solution

(16)  (1/2) + (1/3) - (1/4)  = 

(A)  1/20  (B)  7/12  (C)  3/4  (D)  1  (E)  13/12

Solution

(17)  In the diagram, AC  =  BD  =  17 and BC  =  3. The length of segment AD is 

(A)  20  (B)  24  (C)  28  (D)  31  (E)  34

Solution

(18)  What is the value of |x - y| + |y - x| if x = -3 and y = -7 ?

(A)  -14  (B)  -6  (C)  0  (D)  8  (E)  20

Solution

(19)  The product of the first ten prime numbers must be divisible by

(A)  16  (B)  18  (C)  20   (D)  22  (E)  24

Solution

(20)   4³ + 4³ +4³ + 4³  =  

(A)  4⁴  (B)  4⁹  (C)  4¹²  (D)  16³  (E)  16¹²

Solution