PSAT MATH PRACTICE TEST ONLINE

Question 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 :

Total number of of words in one page  =  750

Number of words in 6 pages  =  6(750)  =  4500

300 words can be read in 3 minutes.

Number of words read in 1 minute  =  300/3  =  100

Number of minutes taken to read 4500 words 

  =  4500/100

  =  45 minutes 

Question 2 :

[(1/2) - (3/4)]² + (5/10)  =  

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

Solution :

=  [(1/2) - (3/4)]² + (5/10)

=  [(2-3)/4]² + (5/10)

=  (-1/4)² + (1/2)

=  1/16 + 1/2

=  (1 + 8)/ 16

=  9/16

Hence the answer is 9/16.

Question 3 :

If x = 2⁵ ⋅ 3² ⋅ 7, then what is the value of x ?

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

Solution :

x = 2⁵ ⋅ 3² ⋅ 7

x  =  (32) ⋅ 9 ⋅ 7

x  =  2016

Question 4 :

A right cylindrical can is being filled with water. At 1 P.M, it is half full. At 2 P.M, it is 3/4 ^th 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 :

From the given information, we know that for every 1 hour 1/4 th of the tank is being filled.

At 1 P.M, 1/2 of the tank is being filled

At 2 P.M, 3/4 of the tank is being filled

At 3 P.M, full tank is being filled

At 12 P.M, 1/4 of the tank is being filled

At 11 A.M, the tank is empty.

Question 5 :

If x⁸  =  (2²) ⁴, what is x² ?

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

Solution :

x⁸  =  (2²) ⁴

x⁸  =  2⁸

Since the powers are equal, we may equate the base.

x = 2

x²  =  2²  =  4 

Question 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 :

Fraction of work left  =  1 - (1/8)

=  (8 - 1)/8

=  7/8

Question 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 :

Number of steps required to reach from 1 to 2 in solid line  =  4

Number of steps required to reach from 1 to 2 in dotted line  =  3

  =  3 - 4

  =  -1

Question 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 :

To find how much bigger is Jakie's way than Jesse's way

  =    8 - √34

Question 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 :

The value of θ cannot be ∞, from the given choices, in option B we have 0 for i. By applying this value, we get  ∞. 

Hence option B is the answer.

Question 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 :

Height of James in Monday  =  20 inches

in Tuesday  =  40 inches

in Wednesday  =  60 inches

  =  60 - 20

  =  40 inches

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