# HSPT Quantitative : Number Manipulation*

## Example Questions

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### Example Question #1 : How To Manipulate Numbers

What number is the square of 4 divided by 2?

Explanation:

First, square 4.

Then divide the answer by two.

### Example Question #2 : How To Manipulate Numbers

What number is the cube of 4 multiplied by 2?

Explanation:

First, cube 4.

### Example Question #1 : How To Manipulate Numbers

What number divided by 5 is of 40?

Explanation:

Set up an equation that fits the information:

### Example Question #4 : How To Manipulate Numbers

What number is 4 times of 80?

Explanation:

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

### Example Question #2 : How To Manipulate Numbers

What number divided by  is  percent of ?

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 #3 : How To Manipulate Numbers

is  percent of what number?

Explanation:

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

### Example Question #4 : How To Manipulate Numbers

What number is   of  less than ?

Explanation:

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

Then,  of  is :

### Example Question #1 : How To Manipulate Numbers

What number is  percent of the difference between  and ?

Explanation:

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

Then,  percent of that is :

### Example Question #9 : How To Manipulate Numbers

What number is  percent of ?

Explanation:

Multiply  by  to find  percent:

### Example Question #10 : How To Manipulate Numbers

What is the average of  and ?