### All HSPT Quantitative Resources

## Example Questions

### Example Question #21 : Number Manipulation*

What is the difference between and ?

**Possible Answers:**

**Correct answer:**

First, square the numbers:

Then, subtract to find the difference:

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

What is the average of , , and ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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

Then, multiply by three to reverse the division:

### Example Question #22 : Number Manipulation*

is what percent of ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

The formula for circumference is .

For the first circle:

And for the second:

The ratio is then , or .

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

What is percent of the product of and ?

**Possible Answers:**

**Correct answer:**

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

Second, percent of that is:

### Example Question #21 : Number Manipulation*

What number is more than of ?

**Possible Answers:**

**Correct answer:**

First, of is , because .

Then, add :

### Example Question #22 : Number Manipulation*

What number divided by equals of ?

**Possible Answers:**

**Correct answer:**

First, of is because .

Then, multiply by to reverse the division:

### Example Question #29 : Number Manipulation*

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

**Possible Answers:**

**Correct answer:**

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

### Example Question #25 : How To Manipulate Numbers

What number added to makes of ?

**Possible Answers:**

**Correct answer:**

of is , because . Then, subtract to find the answer: