# HSPT Quantitative : How to manipulate numbers

## Example Questions

### Example Question #51 : Number Manipulation*

What is  of  less than ?

Explanation:

First, find   less than :

Then, find :

### Example Question #52 : Number Manipulation*

is  percent of what number number?

Explanation:

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

### Example Question #53 : How To Manipulate Numbers

What is  percent of ?

Explanation:

First, square :

Then, find  percent:

### Example Question #53 : Number Manipulation*

What number multiplied by  equals  more than  of ?

Explanation:

First, find  of :

Finally, divide by  to reverse the multiplication:

### Example Question #54 : Number Manipulation*

What is  percent of  of ?

Explanation:

First, find  of :

Then, find  percent:

### Example Question #56 : How To Manipulate Numbers

What is the average of  and ?

Explanation:

Find the average by adding the numbers and dividing by :

### Example Question #55 : Number Manipulation*

What is  less than  of ?

Explanation:

First, find  of :

Then, subtract :

### Example Question #56 : Number Manipulation*

What is the product of  and  percent of ?

Explanation:

The square of  is :

percent of  is :

Multiply these to find the product:

### Example Question #53 : Number Manipulation*

What is  percent of ?

Explanation:

Multiply  by the decimal equivalent of the percentage to find the answer:

### Example Question #51 : How To Manipulate Numbers

What is  less than  of ?