Given the numbers 18, 15, 23, - 14, and 1120,… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Fractions/Ratios/Decimals

Given the numbers $\frac{1}{8}$ , $\frac{1}{5}$ , $\frac{2}{3}$ , $-\frac{1}{4}$ , and $\frac{1}{120}$ , if one more number is added to the group and the average increases by $\frac{1}{20}$ , what is the value of that number?

Correct answer marked below

\frac{1}{20}

\frac{1}{5}

\frac{1}{4}

\frac{3}{8}

\frac{9}{20}

Correct

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Explanation

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Official Explanation

Official

Method 1:

Sum of the 5 numbers =

\frac{1}{8} + \frac{1}{5} + \frac{2}{3} - \frac{1}{4} + \frac{1}{120} = \frac{15 + 24 + 80 - 30 + 1}{120} = \frac{90}{120} = \frac{3}{4}

Mean of the 5 numbers =

\frac{3}{4} \div 5 = \frac{3}{20}

Assuming the number as

n

, since the average increases by

\frac{1}{20}

, we have:

\frac{\frac{3}{4} + n}{6} = \frac{3}{20} + \frac{1}{20}

\Rightarrow \frac{3}{4} + n = \frac{4}{20} \times 6

\Rightarrow \frac{3}{4} + n = \frac{24}{20}

\Rightarrow n = \frac{24}{20} - \frac{3}{4} = \frac{24}{20} - \frac{15}{20} = \frac{9}{20}

Method 2 (educated guess approach):

The group has 5 numbers. On adding the new number, the average increases by

\frac{1}{20}

.…

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What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.