### All HSPT Quantitative Resources

## Example Questions

### Example Question #1 : How To Manipulate Numbers

What number is the square of 4 divided by 2?

**Possible Answers:**

**Correct answer:**

First, square 4.

Then divide the answer by two.

### Example Question #1 : How To Manipulate Numbers

What number is the cube of 4 multiplied by 2?

**Possible Answers:**

**Correct answer:**

First, cube 4.

Multiply that answer by 2.

### Example Question #2 : How To Manipulate Numbers

What number divided by 5 is of 40?

**Possible Answers:**

**Correct answer:**

Set up an equation that fits the information:

### Example Question #3 : How To Manipulate Numbers

What number is 4 times of 80?

**Possible Answers:**

**Correct answer:**

Set up an equation using the information provided, and then solve.

### Example Question #4 : How To Manipulate Numbers

What number divided by is percent of ?

**Possible Answers:**

**Correct answer:**

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

Now, multiply this by to reverse the division.

, so the answer is 180.

### Example Question #5 : How To Manipulate Numbers

is percent of what number?

**Possible Answers:**

**Correct answer:**

Using to represent the unknown number, we know that . Using algebraic manipulation, divide both sides by to find .

### Example Question #6 : How To Manipulate Numbers

What number is of less than ?

**Possible Answers:**

**Correct answer:**

Work backwards to solve this problem. First, less than is :

Then, of is :

### Example Question #7 : How To Manipulate Numbers

What number is percent of the difference between and ?

**Possible Answers:**

**Correct answer:**

Work backwards to solve this problem. First, the difference between and is :

Then, percent of that is :

### Example Question #9 : How To Manipulate Numbers

What number is percent of ?

**Possible Answers:**

**Correct answer:**

Multiply by to find percent:

### Example Question #10 : How To Manipulate Numbers

What is the average of and ?

**Possible Answers:**

**Correct answer:**

The first step is to calculate the squares:

Second, find the average by finding the sum and dividing by the number of numbers: