# HSPT Quantitative : How to manipulate numbers

## Example Questions

### Example Question #21 : How To Manipulate Numbers

What is the difference between  and ?

Explanation:

First, square the numbers:

Then, subtract to find the difference:

### Example Question #21 : How To Manipulate Numbers

What is the average of , and ?

Explanation:

First, .

Then, find the sum and divide by the number of elements:

### Example Question #21 : How To Manipulate Numbers

is  percent of what number divided by ?

Explanation:

First, find the number that  is  percent of. We will call that unknown number :

Then, multiply by three to reverse the division:

### Example Question #21 : How To Manipulate Numbers

is what percent of  ?

Explanation:

Using  to represent the unknown percentage, we can say that .

Divide both sides by  to find :

Rewritten as a percent,  is  percent.

### Example Question #21 : Number Manipulation*

What is the ratio of the circumference of a circle with a radius of  to the circumference of a circle with a radius of ?

Explanation:

The formula for circumference is .

For the first circle:

And for the second:

The ratio is then , or .

### Example Question #22 : Number Manipulation*

What is  percent of the product of  and ?

Explanation:

Work backwards to solve this problem. First, the product of   and  is:

Second,  percent of that is:

### Example Question #23 : Number Manipulation*

What number is  more than  of ?

Explanation:

First,  of  is , because .

### Example Question #24 : Number Manipulation*

What number divided by  equals  of ?

Explanation:

First,   of  is  because .

Then, multiply by  to reverse the division:

### Example Question #21 : How To Manipulate Numbers

What number is twice as much as the square root of ?

Explanation:

The square root of  is  because . Next, multiply by  to find twice as much:

### Example Question #22 : How To Manipulate Numbers

What number added to  makes  of ?