# PSAT MATH PRACTICE TEST QUESTIONS WITH ANSWERS

Question 1 :

What is the value of r in the equation 2r  = 102 ?

(A)  5  (B)  10  (C)  25  (D)  50  (E)  100

Solution :

2r  = 102

2r  = 100  ==>  r  =  100/2  ==>  50

Hence the value of r is 50.

Question 2 :

What is the area of a square with a perimeter of 16 ?

(A)  4  (B)  8  (C)  12  (D)  16  (E)  24

Solution :

Perimeter of square  =  16

4a  =  16

a  =  16/4  =  4

Area of square  =  a2

=  42  =  16

Question 3 :

What is 10% of a number whose square is 81 ?

(A)  0.81  (B)  0.9  (C)  8.1  (D)  9  (E)  10

Solution :

Let "x" be the unknown number

Given that:

Square of the unknown number  =  81

x2  =  81

x  =  9

10% of x  =  (10/100) ⋅ 9

=  9/10

=  0.9

Question 4 :

What is the range of the set {1, 2, 5, 10, 6, 12} ?

(A)  -16  (B)  -11  (C)  3  (D)  11  (E)  22

Solution :

To find the range of the given set, we have to subtract the smallest value from the largest value.

Range  =  L - S

Largest value  =  12, Smallest value  =  1

R  =  12 - 1  =  11

Hence the range is 11.

Question 5 :

Nancy found a formula for the area of a square in terms of its perimeter. Let A stand for the area and P for perimeter. What is the formula Nancy found ?

(A)  p2  (B)  p2/8  (C)  p2/4  (D)  p2/16  (E)  4p

Solution :

A - Area of square

P - Perimeter of square = 4a

A  =  a2 and P = 4a  ==> a  =  P/4

Applying the value of a in area of square formula, we get

A  =  (p/4)2  =  P2/16

Question 6 :

Anayet is driving to work from home and realizes he left his wallet at home when he is at workplace. He turns back to retrieve his wallet. His workplace and home are 45 miles apart and it takes him twice as long to get to workplace from his home than the other way around. It is a 30 minutes drive from his workplace to home. What is the average speed for the round trip in miles per minute ?

(A)  0.75   (B)  1.5  (C)  1  (D)  2  (E)  0.5

Solution :

Distance between workplace and home  =  45 miles

Time taken to drive from his workplace to home

=  30 minutes

Given that :

Going back to home, retrieving his wallet and coming back to workplace is twice as long.

Distance covered  =  2(45)  =  90 miles

Time taken  =  30 + 30 + 30  =  90 minutes

Average speed  =  Distance / Time

=  90/90

=  1 minute/mile.

Hence the average speed is 1 minute/mile.

Question 7 :

Given that a vector  =  a2 + a, what is a vector  ÷ a ?

(A)  a  (B)  a + 2  (C)  1  (D)  a + 1  (E)  2a

Solution :

a vector  ÷  a  =  (a2 + a) /a

=  a(a + 1)/a

=  a + 1

Question 8 :

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

1 is 2 times than 1/2.

Hence 2 times is the answer.

Question 9 :

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 to zero, it will become the same number. By squaring 0, we get 0.

Question 10 :

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.

Note : There are infinite numbers between 3 and 5.

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