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 :
|
Jackie's way : √(a + b) = √a + √b a = 9 and b = 25 √(a + b) = √9 + √25 = 3 + 5 = 8 |
Jesse's way : √(a + b) = √(a+b) a = 9 and b = 25 √(a + b) = √(a+b) = √(9+25) = √34 |
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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