PSAT MATH TEST PREPARATION

Question 1 :

What is the value of √25 + √64 ?

(A)  10     (B)  13    (C)  14    (D)  89

Solution :

√25  =  √(5 ⋅ 5)  =  5

√64  =  √(8 ⋅ 8)  =  8

  =  5 + 8

√25 + √64   =  13

Question 2 :

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

(A)  10     (B)  25    (C)  50    (D)  1003

Solution :

2r  = 10²

2r  = 100  ==>  r  =  100/2  ==>  50

Hence the value of r is 50.

Question 3 :

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

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

Solution :

Perimeter of square  =  16

4a  =  16

a  =  16/4  =  4

Area of square  =  a²

  =  4²  =  16

Question 4 :

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

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

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 5 :

What is the range of the values given below ?

2, 5, 7, 12, 9, 11, 1, 10 

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

Solution :

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

That is, 

Range  =  L - S

Here, Largest value  =  12, Smallest value  =  1

Then, we have

Range  =  12 - 1

Range  =  11

Question 6 :

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)  p²/8     (B)  p²/4    (C)  p²/16    (D)  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

Hence the answer is P²/16.

Question 7 :

Anayet is driving to work from home and realizes he left his wallet at home when he is at his 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 minute 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

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 8 :

What is the difference between the largest and lowest integer in the sequence of consecutive odd integers whose sum is 15 ?

(A)  2     (B)  4     (C)  5    (D)  9

Solution :

The sequence 3, 5, 7 adds upto 15. The difference between 7 and 3 is 4.

Question 9 :

What is the value of (9⁴ - 8⁴)/(9² + 8²)

(A)  8     (B)  12     (C)  15    (D)  17

Solution :

=  [(9²)² - (8²)²] / (9² + 8²)

=  [(9² + 8²)(9² - 8²)] / (9² + 8²)

=  (9²) - (8²)

=  81 - 64

=  17

Question 10 :

Jackie fills a jug with water continuously. It takes her 2 minutes to fill up 50% of the empty space in the jug with water. After every 2 minutes, she puts a penny into a jar to celebrate. How many pennies will she have in the jar at the instant the jug has less than 30% empty space left ?

(A)  0     (B)  1     (C)  2    (D)  33

Solution :

At the first round, he fills 50% of empty space in the jug in 2 minutes and drop a penny.Now the jug contains 50% of empty space.

If he fills half of the 50% of empty space at that instant, the quantity of water will become 75%. But there will be 25% of empty space.  Hence the condition will not satisfy, by filling water in the second round.

So, there is only 1 penny in the jar at the instant the jug has lesser than  30% of empty space.

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