HSPT Quantitative : How to manipulate numbers

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

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Example Question #1 : How To Manipulate Numbers

What number is the square of 4 divided by 2?

Possible Answers:

\dpi{100} 1

\dpi{100} 16

\dpi{100} 8

\dpi{100} 4

Correct answer:

\dpi{100} 8

Explanation:

First, square 4.

\dpi{100} 4^{2}=16

Then divide the answer by two.

\dpi{100} \frac{16}{2}=8

Example Question #2 : How To Manipulate Numbers

What number is the cube of 4 multiplied by 2?

Possible Answers:

\dpi{100} 64

\dpi{100} 128

\dpi{100} 24

\dpi{100} 32

Correct answer:

\dpi{100} 128

Explanation:

First, cube 4.

\dpi{100} 4^{3}=64

Multiply that answer by 2.

\dpi{100} 2\times 64=128

Example Question #2 : How To Manipulate Numbers

What number divided by 5 is \dpi{100} \frac{1}{8} of 40?

Possible Answers:

\dpi{100} 20

\dpi{100} 40

\dpi{100} 25

\dpi{100} 5

Correct answer:

\dpi{100} 25

Explanation:

Set up an equation that fits the information:

\dpi{100} \frac{x}{5}=\frac{1}{8}\cdot 40

\dpi{100} \frac{x}{5}=5

\dpi{100} 5\cdot \frac{x}{5}=5\cdot 5

\dpi{100} x=25

Example Question #3 : How To Manipulate Numbers

What number is 4 times \dpi{100} \frac{1}{8} of 80?

Possible Answers:

\dpi{100} 3200

\dpi{100} 20

\dpi{100} 40

\dpi{100} 32

Correct answer:

\dpi{100} 40

Explanation:

Set up an equation using the information provided, and then solve.

\dpi{100} x=4\cdot (\frac{1}{8}\cdot 80)

\dpi{100} x=4\cdot 10

\dpi{100} x=40

Example Question #4 : How To Manipulate Numbers

What number divided by  is  percent of ?

Possible Answers:

Correct answer:

Explanation:

Work backwards to solve this problem. First,  percent of  is , because .

Now, multiply this by  to reverse the division.

, so the answer is 180.

Example Question #5 : How To Manipulate Numbers

 is  percent of what number?

Possible Answers:

Correct answer:

Explanation:

Using  to represent the unknown number, we know that . Using algebraic manipulation, divide both sides by  to find .

Example Question #6 : How To Manipulate Numbers

What number is   of  less than ?

Possible Answers:

Correct answer:

Explanation:

Work backwards to solve this problem. First,  less than  is :

Then,  of  is :

Example Question #7 : How To Manipulate Numbers

What number is  percent of the difference between  and ?

Possible Answers:

Correct answer:

Explanation:

Work backwards to solve this problem. First, the difference between  and  is :

Then,  percent of that is :

Example Question #8 : How To Manipulate Numbers

What number is  percent of ?

Possible Answers:

Correct answer:

Explanation:

Multiply  by  to find  percent:

Example Question #9 : How To Manipulate Numbers

What is the average of  and ?

Possible Answers:

Correct answer:

Explanation:

The first step is to calculate the squares:

Second, find the average by finding the sum and dividing by the number of numbers:

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