# HSPT Quantitative : How to manipulate numbers

## Example Questions

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### Example Question #211 : Number Manipulation*

Which statement is correct?

Explanation:

By the order of operations, each expression is evaluated by carrying out the operation in parentheses first:

Therefore, .

### Example Question #211 : How To Manipulate Numbers

What is forty percent of the square of nine?

Explanation:

The square of nine is .

Forty percent of a number is equal to the number multiplied by , so forty percent of 81 is

.

### Example Question #211 : How To Manipulate Numbers

If twenty is subtracted from a number, the difference is equal to the same number divided by two. What is this number?

Explanation:

If we let  be the number in question, "twenty...subtracted from a number" can be rewritten as ; "the same number divided by two" can be rewritten as . The two are equal, so we solve the equation

One way to solve this is to first multiply both sides by two to eliminate the fraction:

Distribute:

Subtract  from, and add 40 to, both sides:

.

### Example Question #213 : Number Manipulation*

What number, multiplied by , is  of  of

Explanation:

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

Then find  of that:

Finally, divide by  to reverse the multiplication:

### Example Question #215 : How To Manipulate Numbers

is  percent of what number?

Explanation:

Set up a proportion to solve this problem:

Cross multiply and solve:

### Example Question #561 : Hspt Quantitative Skills

What is the difference between  and ?

Explanation:

First, calculate the exponents:

Subtract to find the difference:

### Example Question #214 : Number Manipulation*

What number, when multiplied by , equals the product of  and ?

Explanation:

First find the product of  and :

Then divide by :

### Example Question #215 : Number Manipulation*

What is  less than the product of  and ?