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by swerve » Tue Aug 07, 2018 10:25 am

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Source: e-GMAT

A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in milliliters) so that the resulting solution contains 60% alcohol?

1. Total quantity of the resulting solution is 350 milliliters.
2. The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water.

The OA is A.
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by Jay@ManhattanReview » Tue Aug 07, 2018 9:59 pm
swerve wrote:Source: e-GMAT

A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in milliliters) so that the resulting solution contains 60% alcohol?

1. Total quantity of the resulting solution is 350 milliliters.
2. The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water.

The OA is A.
Given: Ratio of alcohol to water in the solution is 7 : 3
Question: How much water should be added to the solution so that the resulting solution contains 60% alcohol?

Say alcohol = 7x ml and water = 3x ml and y ml water is added to make the solution containing 60% alcohol.

=> Alcohol / (Water + Additional water) = 60%

7x / (3x + y) = 3/5

=> 5x = 3y

If we get the value of x, we get the answer.

Let's take each statement one by one.

1. Total quantity of the resulting solution is 350 milliliters.

=> 7x + 3x + y = 10x + y = 350

From 10x + y = 350 and 5x = 3y, we can get the unique value of y. Sufficient.

2. The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water.

Alcohol : Water : : 10.5 : 4.5
Alcohol : Water : : 105 : 45
Alcohol : Water : : 7 : 3

This is the same information that we know from the question. No additional information. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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