The ratio of cranberry to apple to orange jui… | GMAT Sprint

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PS · Problem Solving

705-805

Fractions/Ratios/Decimals

The ratio of cranberry to apple to orange juice in a certain cocktail containing no other liquids is x: 5: 3. After 6 gallons of water are added to the cocktail, the ratio of orange juice to total liquid becomes 1: 4. After another 24 gallons of water are added to the cocktail, the ratio of apple juice to total liquid becomes 1: 4. What fraction of the original cocktail is cranberry juice?

Answer Choices

Correct answer marked below

1/5

Correct

1/4

1/3

1/2

2/3

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Explanation

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Official Explanation

Official

Let the original amounts be: cranberry =

kx

, apple =

5k

, orange =

3k

gallons, where

k

is a positive constant.

Total original liquid =

k(x+5+3) = k(x+8)

gallons.

After adding 6 gallons of water:

Total liquid =

k(x+8)+6

.

Orange juice =

3k

.

Given:

\frac{3k}{k(x+8)+6} = \frac{1}{4}

.

Cross-multiply:

12k = k(x+8)+6

.

So:

12k = kx + 8k + 6

.

Rearrange:

12k - 8k - kx = 6

→

4k - kx = 6

→

k(4-x) = 6

. (Equation 1)

After adding another 24 gallons of water (total water added = 6+24 = 30 gallons):

Total liquid =

k(x+8)+30

.

Apple juice =

5k

.

Given:

\frac{5k}{k(x+8)+30} = \frac{1}{4}

.

Cross-multiply:

20k = k(x+8)+30

.…

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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.