A solution that is 20% acetic acid by volume… | GMAT Sprint

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705-805

Fractions/Ratios/Decimals

A solution that is 20% acetic acid by volume is mixed with a solution that is 50% acetic acid by volume, resulting in a mixture that is 40% acetic acid by volume. This 40% solution is then mixed with a solution that is 10% acetic acid by volume, resulting in a solution that is 20% acetic acid by volume. What is the ratio of the volume of the 50% solution of acetic acid to the volume of the 10% solution of acetic acid?

Correct answer marked below

1:3

Correct

1:2

1:1

2:1

3:1

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Explanation

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Official Explanation

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Let:

Volume of solution that is 20% acetic acid =

a

Volume of solution that is 50% acetic acid =

b

Volume of solution that is 10% acetic acid =

c

First mixture: 20% and 50% solutions give 40% mixture.

\frac{0.2a + 0.5b}{a + b} = 0.4

0.2a + 0.5b = 0.4(a + b)

0.2a + 0.5b = 0.4a + 0.4b

0.1b = 0.2a

b = 2a

Second mixture: The 40% mixture (total volume

a+b

) is mixed with the 10% solution to give 20% mixture.…

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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.