# HSPT Quantitative : How to manipulate numbers

## Example Questions

### Example Question #201 : How To Manipulate Numbers

A number divided by the sum of 25 and 7 is equal to . What is that number?

Explanation:

The sum of 25 and 7 is , so "a number divided by the sum of 25 and 7 is equal to ." can be restated as "a number divided by 32 is equal to . ". This can be rewritten as

,

which can be solved by multiplying both sides by 32, thereby isolating :

Rewrite as improper fractions and multiply across, then reduce:

### Example Question #201 : How To Manipulate Numbers

Which of the following is not equal to 30?

(a) 20% of 150

(b)  of 150

(c)

(b)

All three expressions are equal to 30.

(a)

(c)

(c)

Explanation:

(a) 20% of 150 is equal to the decimal equivalent of 20%, which is 0.20, multiplied by 150:

(b)  of 150 can be calculated as follows:

(c)

(c) is the correct response.

### Example Question #202 : How To Manipulate Numbers

What number increased by 15% is equal to 230?

Explanation:

If  is the number in question, then 15% of the number is

Increasing a number by 15% is equivalent to adding  to ; since this is equal to 230, this sets up the equation

Collect like terms:

Multiply both sides by :

.

### Example Question #551 : Hspt Quantitative Skills

Subtract the square root of 144 from the square of 144.

Explanation:

Since , the square root of 144 is 12 (there are actually two square roots, 12 and , but "the" square root refers to the positive root).

The square of 144 is

Subtract 12 from 20,736:

### Example Question #205 : How To Manipulate Numbers

Add the square root of 36 to the square of 6.

Explanation:

; therefore, the square of 6 is 36, and the square root of 36 is 6 (36 actually two square roots, 6 and , but "the" square root refers to its positive square root). Adding the square root of 36 to the square of 6 is the same as adding 6 to 36, so add:

.

### Example Question #203 : How To Manipulate Numbers

20% of a number is equal to the square root of 36. What is the number?

Explanation:

If  is the number in question, "20% of a number" can be written as , or, in lowest terms, .

Also, since , 36 has 6 as its square root (there are actually two square roots, 6 and , but "the" square root refers to the positive root). Therefore, "20% of a number is equal to the square root of 36" can be reworded as "20% of a number is equal to 6", and written as the equation

Multiply both sides by 5:

### Example Question #202 : How To Manipulate Numbers

Two thirds of a number is equal to two times forty. What is that number?

Explanation:

Let  be the number in question. "Two thirds of a number is equal to two times forty" translates as the equation

Multiply on the right:

Multiply both sides by  to isolate :

### Example Question #205 : How To Manipulate Numbers

Add one fourth of 26 to one third of 33. What is the result?

Explanation:

"Add[ing] one fourth of 26 to one third of 33" means to evaluate the expression

By the order of operations, perform the leftmost multiplication first:

Perform the rightmost multiplication next:

### Example Question #203 : How To Manipulate Numbers

Ten times a number is twenty more than six times that same number. What is the number?

Explanation:

Letting  the unknown number, "ten times a number is twenty more than six times that same number" can be written as the algebraic equation

Subtract  from both sides:

Collect like terms:

Divide both sides by 4, thereby isolating the :

Evaluate:

30% of