In an election involving only 2 candidates, 1… | GMAT Sprint

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PS · Problem Solving

705-805

Fractions/Ratios/Decimals

In an election involving only 2 candidates, 1/9 of the total voters did not cast their vote. 1/11 of the votes polled were declared invalid. The losing candidate got 33.5% of the valid votes polled and lost by 38400 votes. The number of total voters enrolled on the voter list was?

Answer Choices

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108000

132000

136000

144000

Correct

156000

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Explanation

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Official Explanation

Official

This is a fraction problem.

It is mentioned in the question that

\frac{1}{9}

of the voters did not cast their vote, which means

\frac{8}{9}

of the voters cast their votes.

Let total voters =

x

Votes cast =

\frac{8x}{9}

Invalid votes =

\frac{1}{11}

of votes cast =

\frac{1}{11} \times \frac{8x}{9} = \frac{8x}{99}

Valid votes = votes cast − invalid votes =

\frac{8x}{9} - \frac{8x}{99} = \frac{88x}{99} - \frac{8x}{99} = \frac{80x}{99}

Losing candidate got

33.5\%

of valid votes, so winning candidate got

100\% - 33.5\% = 66.5\%

of valid votes.…

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What this question tests

What it tests

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

Common trap

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