# HSPT Quantitative : How to manipulate numbers

## Example Questions

### Example Question #41 : How To Manipulate Numbers

What number is  less than  percent of ?

Explanation:

First, find   percent of :

Then, subtract :

### Example Question #42 : How To Manipulate Numbers

What is  less than  of ?

Explanation:

First, find   of :

Then, subtract :

### Example Question #43 : How To Manipulate Numbers

What is  percent of  percent of ?

Explanation:

percent of  is :

percent of  is :

### Example Question #41 : How To Manipulate Numbers

What is the difference between  and ?

Explanation:

First, calculate the exponents:

Then subtract to find the difference:

### Example Question #45 : How To Manipulate Numbers

What is the average of , and ?

Explanation:

To calculate the average, you can add up the three numbers and divide by three (the number of elements):

Also, if the numbers are evenly spaced, the middle number will be the average.

### Example Question #42 : How To Manipulate Numbers

What number is  less than  of ?

Explanation:

First, find  of :

Then, subtract :

### Example Question #44 : How To Manipulate Numbers

is  percent of what number?

Explanation:

Representing the unknown number with an , we know that . Solve for  by dividing both sides by :

### Example Question #43 : How To Manipulate Numbers

What number, when divided by , is  of ?

Explanation:

First, find   of :

Then, multiply by  to reverse the division:

### Example Question #45 : How To Manipulate Numbers

What is  of  percent of ?

Explanation:

First, find   percent of :

Then, find  of that:

### Example Question #46 : How To Manipulate Numbers

What is  of  less than ?

Explanation:

First, subtract  from :

Then, find :