PSAT MATH QUESTION PAPER WITH SOLUTIONS

(1)  It takes George 3 minutes to read 300 words. If each page in a book that he is reading has 750 words, how long will it take George to read 6 pages ?

(A)  30 minutes  (B)  45 minutes  (C)  60 minutes 

(D)  90 minutes  (E)  250 minutes

Solution

(2)  [(1/2) - (3/4)]2 + (5/10)  =  

(A)  9/16  (B)  1/2  (C)  1/16  (D)  3/4  (E)  1/4

Solution

(3)  If x = 25 ⋅ 3⋅ 7, then what is the value of x ?

(A)  1150  (B)  2000  (C)  2015  (D)  2016  (E)  3050

Solution

(4)  A right cylindrical can is being filled with water. At 1 P.M, it is half full. At 2 P.M, it is 3/4th full. At this rate, when was it empty ?

(A)  11 : 00 A.M  (B)  11 : 30 A.M  (C)  12 : 00 P.M

(D)  12 : 30 P.M  (E)  3 : 00  P.M

Solution

(5)  If x8  =  (22) 4, what is x2 ?

(A)  2  (B)  4  (C)  8  (D)  64  (E)  128

Solution

(6)  James has a work to finish. He finishes 1/8 of the total work on the first day. What fraction of the work is left ?

(A)  1/8  (B)  3/8  (C)  7/8  (D)  3/4  (E)  1/4

Solution

(7)  

There are two different pathways connecting 1 and and 2. How many fewer steps is the solid line path than the dotted line path. (A step is defined as a line segment connecting 2 circles)

(A)  -4  (B)  -1  (C)  1  (D)  4  (E)  7

Solution

(8)  Jackie and Jesse each solve the same problem in a different way 

Problem √(a + b)  =  ?

Jackie's way  =  √(a + b)  =  √a + √b

Jesse's way : √(a + b)  =  √(a+b)

If a = 9 and b = 25, how much bigger is Jakie's way than Jesse's way ?

(A)  -2  (B)  0  (C)  2  (D)  √36  (E)  8 - √34

Solution

(9)  If  θ { a, b, c, d, e, f, g, h, i }  =  [ab - cd + (ef)2 (gh)2]/i

Which cannot be value of θ ?

(A)  θ (0, 0, 0, 0, 0, 0, 0, 0, 1)

(B)  θ (1, 1, 1, 1, 1, 1, 1, 1, 0)

(C)  θ (2, 2, 2, 2, 2, 2, 2, 2, 10)

(D)  θ (2,3, 1, 4, 5, 6, 7, 0, 10)

(E)  0

Solution

(10)  If James grows by 20 inches every day starting Monday. What is the difference in his height between Wednesday and Monday ?

(A)  0 inches  (B)  20 inches  (C)  30 inches 

(D)  40 inches  (E) 60 inches

Solution

(11)  Evaluate ([1/2)-(3/4)] ÷ (1/2)  =  

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

Solution

(12)  

Line q intersects the parallel lines p and l. What is y3/3 ?

(A)  x4/3  (B)  x6  (C)  x9  (D)  x4/9  (E)  x6/3

Solution

(13)   Given the arithmetic sequence x, y, 30, z, f then find the value of x + y + z + f

(A)  60  (B)  80  (C)  120  (D)  130  (E)  140

Solution

(14)  If (-1)2  =  1, then the value (-1) 2023 is

(A)  -2023  (B)  -1  (C)  0  (D)  1  (E)  2023

Solution

(15)  Caroline has two times as many marbles as Jake. Jake has 12 less than 7 times as many marbles James has. James has 14 marbles. How many marbles dies Caroline have ?

(A)  52  (B)  54  (C)  86  (D)  98  (E)  172

Solution

(16)  John is trying to escape a ditch. Every time he jumps 10 meters, he falls back 5 meters right after. The ditch is 19 meters long. What is the minimum number of jumps he needs to make to escape ?

(A) 3  (B) 4  (C) 5  (D) 7  (E) 8

Solution

(17)  What is the largest number of digits that the product of  3 digit and 2 digit number has ?

(A)  4  digit  (B)  5 digit  (C)  6 digit 

(D)  7 digit  (E)  8 digit

Solution

(18)  If Fn  =  2 Fn-1 + 3 Fn-2, then what is F3 if F =  F2  =  1 ?

(A)  2  (B)  3  (C)  4  (D)  5  (E)  10

Solution

(19)  Sam walks 3m to the west, then 4m south, then 4 m North. How far is he from his original location ?

(A)  3 m (B)  5 m (C)  7 m  (D)  8 m  (E)  12 m

Solution

(20)  If a =  3 and b = 5, what is the value of 9a/(b-a) ?

(A)  9  (B)  27  (C)  13/5  (D)  27/2  (E)  26/5

Solution

If you would like to have more questions on PSAT math, please click on the links given below.

PSAT online practice test math - Paper 1

PSAT online practice test math - Paper 2

PSAT online practice test math - Paper 3

PSAT online practice test math - Paper 4

PSAT online practice test math - Paper 5

PSAT online practice test math - Paper 6

PSAT online practice test math - Paper 7

PSAT online practice test math - Paper 8

PSAT online practice test math - Paper 9

PSAT online practice test math - Paper 10

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