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

(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

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

(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