PSAT MATH WORKSHEET

Question 1 :

The circle that is inscribed in the square below has a radius of 2. What is the length of diagonal of the square ?

(A)  2  (B)  4  (C)  16  (D)  4√2  (E)  2√2

Solution :

Side length of square  =  4 Length of diagonal    =  √(42 + 42)    =  √32    =  4√2

Question 2 :

What is the absolute value of the difference between the number of integers between 0 and 5 inclusive and the number of integers between 1 and 6 exclusive ?

(A)  0  (B)  1  (C)  2  (D)  3  (E)  5

Solution :

Integers between 0 and 5 inclusive. 

0, 1, 2, 3, 4, 5

There are 6 integers.

Integers between 1 and 6 exclusive.

2, 3, 4, 5

There are 4 integers.

Then, 

  =  |6 - 4|

  =  2 integers.

Question 3 :

Corey is walking on a path. Every three steps he takes, he makes a 30 degree rotation to counterclockwise, if he took 18 steps in total, how many full revolutions was he able to make altogether ?

(A)  0.25  (B)  0.5  (C)  1  (D)  2  (E)  5

Solution :

For every 3 steps, he takes 30 degree rotation. First let us find, how many 3 steps are in 18 steps.

=  18/3 

=  6 times

In 6 times, he completes 180 degree.

So, he completes half of the rotation.The answer is 0.5.

Question 4 :

What is 20% of 20% of 20 ?

(A)  0.2  (B)  0.8  (C)  2  (D)  8  (E)  8000

Solution :

  =  20 % of 20% of 20

  =  20% of (20/100) x 20

  =  20% of (400/100)

  =  20% of 4

  =  (20/100) 4

  =  0.8

Question 5 :

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  (E)  12

Solution :

Let us select three numbers 3, 5 and 7.

3 + 5 + 7  =  15

Difference between largest and lowest integer 

=  7 - 3 

=  4

Hence the answer is 4.

Question 6 :

The half life of a substance is the time it takes for a substance to decrease to half its initial amount. If John initially had 100 pounds of goo and ten days later, he only had 25 pounds of goo, what is the half life of the goo ?

(A)  10 days  (B)  5 days   (C)  7.5 days 

(D)  20 days   (E)  25 days

Solution :

In 10 days, the goo decreased by 2 half lives. So each life is 5 days.

Question 7 :

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

(A)  1  (B)  16  (C)  17  (D)  18  (E)  155

Solution :

(9⁴ - 8⁴) / (9² + 8²)  =  [(9²)² - (8²)²] / (9² + 8²)

  =  [(9² + 8²) (9² - 8²)] / (9² + 8²)

  =  9² - 8²

  =  81 - 64 

  =  17

Hence the answer is 17.

Question 8 :

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

(A)  0  (B)  1  (C)  2  (D)  3  (E)  4

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.

Question 9 :

In the figure above, there are two balance beams that have triangles, circles and squares on them. Both beams are fully balanced. How many circles are needed to balance 70 squares ?

(A)  10  (B)  12  (C)  35  (D)  70  (E)  140

Solution :

From the above picture, we know that

1 square = 2 triangles  ---(1)

4 triangles  =  2 circles  ----(2)

Divide by 2 on both sides

2 triangles  =  1 circle  -----(3)

(1) = (3)

1 square  =  1 circle

70 squares  =  70 circles.

So, 70 circles are needed to balance 70 squares.

Question 10 :

 0.7 bar + (2/9)  = 0.6 bar + ____

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

Solution :

Let "x" be 0.7 bar

x  =  0.77777........ ---(1)

Multiply both sides by 10x  =  7.7777.......---(2)

(2) - (1)

10x - x  =  7.7777....... - 0.7777.......

9x  =  7

x  =  7/9

Let "y" be 0.6 bar

y  =  0.66666........ ---(1)

Multiply both sides by 10y  =  6.6666.......---(2)

(2) - (1)

10y - y  =  6.6666....... - 0.6666.......

9y  =  6

y  =  6/9  =  2/3

Hence the answer is 1/3.

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