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 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 R and 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) Evaluate  (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 sum 2¹⁰ + 1¹⁰ + (1/2)¹⁰ + (1/3)¹⁰ + (1/4)¹⁰ is closest to

(A)  21  (B)  32  (C)  513   (D)  1025  (E)  2000

Solution

(20)   4³ + 4³ + 4³ + 4³  =  

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

Solution