How to Pass Numerical Reasoning (28 page)

Or in another arrangement:

When you are working out the answers to the problems, there is often more than one way to arrive at the correct answer. Decide which method is the easiest for you to work with. You can check your answer with an alternative method.

Working with percentages: the part

To find the part when working with a percentage, use the following formula:

Part = Percentage × Whole

Worked example

What is 25% of 25? You are looking for the part of the whole number (25) that equals 25%.

Method 1

Multiply the whole number by the decimal equivalent of the percentage:

25% = 0.25

Method 2

Express the percentage as a fraction over 100 and multiply by the whole number.

Tip:
To find 10% of a number, move the decimal point at the end of the number one place to the left. For example, to find 10% of 57.5 move the decimal point 1 place to the left = 5.75.

Working with percentages: the whole

To find the whole when working with a percentage, use the following formula:

Worked example

25 is 20% of what number? You are looking for a whole number, of which 20% equals 25.

Method 1

When you are working with simple percentages, work out what fraction of the whole quantity the percentage represents. Then calculate by how much you would need to multiply that quantity to obtain the whole.

Therefore:

You know that
¹
⁄
₅
= 25, so multiply
¹
⁄
₅
× 5 to find 100%.

25 × 5 = 125.

Method 2

Set the percentage up as a fraction over 100 and cross-multiply the fractions to find the whole number (
x
):

Cross-multiply each side:

20
x
= 2500

Divide both sides by 20:

x
= 2500 ÷ 20

x
= 125

Working with percentages: the percentage

To find the whole when working with a percentage, use the following formula:

Worked example

What percentage of 240 is 30? You are given the part (30) and the whole number (240) and asked to work out the percentage.

Method 1

Use the formula and substitute actual values:

Reduce the fraction to its lowest terms:

Convert the fraction to a percentage:

Method 2

Set up the part and the whole number as a fraction and cross-multiply the fractions to find the percentage (
x
):

Cross multiply each side of the fraction:

240
x
= 3000

Divide each side by 240: