MATH PSAT PRACTICE TEST

Question 1 :

The prime factors of 232 are ?

(A)  2, 2, 2, 29     (B)  116, 2     (C)  2, 29    (D)  2, 2, 58

Solution :

Hence the distinct prime factors are 2, 2, 2 and 29.

Question 2 :

Find the value of t if t/32  =  x/p

(A)  32p/x     (B)  32/px     (C)  32x/p   (D)  32px

Solution :

t/32  =  x/p

Multiply by 32 on both sides, we get

t  =  32x/p

Question 3 :

If (x + y)²  =  x² + y², then what condition must be true ?

(A)  x + y  =  0    (B)  2x  =  0    (C)  2y  =  0  (D)  xy  =  0

Solution :

Formula for (x + y)²  =  x² + y² + 2xy

In order to make the right hand side as x² + y², we have to the value of xy as 0.

Question 4 :

Sarah has a trick coin that has heads on both sides. She asks he friend John, who believes the coin is fair, to guess what face it will land on. If they flip the coin 100 times, how many times bigger is Sarah's expected probability of the coin landing on heads than John's expected probability of the coin landing on heads ?

(A)  0.25  (B)  0.5  (C)  1  (D)  2  (E)  4

Solution :

According to Sarah's belief probability of getting head =  1 (Sure event)

According to John's belief probability of getting head =  1/2 (Sure event)

1 is 2 times greater than 1/2.

Hence 2 times is the answer.

Question 5 :

What is the square of a number that when added to any number does not change that number's value ?

(A)  0  (B)  0.5  (C)  1  (D)  4  (E)  undefined

Solution :

0 is the number, when we add any number with zero, it will become the same number. By squaring 0, we get 0.

Question 6 :

How many non zero numbers are between 3 and 5 ?

(A)  0  (B)  2  (C)  8  (D)  9  (E)  undefined

Solution :

The question is, how many non zero numbers are between 3 and 5, it should not be decimal.

Hence the answer is undefined.

Question 7 :

What time will it  be 53 hours after 3 : 30 P.M on Thursday ?

(A)  7 : 30 A.M Saturday  (B)  8 : 30 A.M Saturday

(C)  7 : 30 P.M Saturday  (D)  8 : 30 P.M Saturday

(E)  8 : 30 P.M Sunday

Solution :

First let us divide 53 by 24.

3 : 30 PM - 3 : 30 PM (Thursday - Friday)

3 : 30 PM - 3 : 30 PM (Friday - Saturday)

53  =  2 (24) + 5

5 hours after 3 : 30 P.M on Saturday

8 : 30 PM on Saturday

Question 8 :

Samuel scored a 72, 92 and 80 on his first three exams. What is the minimum score he needs to get an average of 85 ?

(A)  85  (B)  90  (C)  93  (D)  96  (E)  100

Solution :

Let "x" be the required score.

(72 + 92 + 80 + x)/4  =  85

(244 + x)  =  340

x  =  340 - 244

x  =  96

Question 9 :

Five out of marbles in a bag are red. What percentage of the marbles is not red ?

(A)  50%  (B)  55%  (C)  60%  (D)  75%  (E)  80%

Solution :

Total number of marbles  =  10

Number of red marble  =  5

Percentage of red marble  =  (5/10) x 100 %

  =  50%

What percentage of the marbles it is not red  =  50%

Question 10 :

√81 √25 + √16  =  

(A)  5  (B)  40  (C)  49  (D)  56  (E)  64

Solution :

  =  √81 √25 + √16

  =  √(9 ⋅ 9) √(5 ⋅ 5) + √(4 ⋅ 4)

  =  (9 ⋅ 5) + 4

  =  45 + 4

  =  49

Hence the answer is 49.

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