A man sold 2 watches, one at a profit of 10% and the other at a loss of 10%. If the selling prices of both were the same, how much percent did he gain or lose on the whole?

Answer Choices

Correct answer marked below

Lost 1%

Correct

Lost 0.5%

Lost 0.1%

Gained 0.1%

Gained 1%

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Explanation

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Official Explanation

Official

In such questions there's always a loss of

\frac{a^2}{100}\%

.

Hence there will be a loss of

\frac{10 \times 10}{100} = 1\%

.

This corresponds to option A.

This is a very interesting mathematical property that's also very easy to derive. I recommend everyone should try it out on their own. If anyone is having trouble with the derivation, do let me know, I'll be happy to help.

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What this question tests

What it tests

Your ability to apply GMAT math concepts to solve a multi-step problem quickly and accurately. At the 705-805 level, accuracy and speed both matter.

Common trap

Overcomplicating the setup — most GMAT problems reward a direct, organized approach over brute calculation.