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Data Interpretation for a ratio problem

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by srikdave » Tue May 17, 2011 8:29 pm
A cake recipe uses a constant ratio of 2 teaspoons vanilla extract to 1 ounce chocolate. If the original recipe, which serves four people, is altered proportionally to yield a cake that serves six people, how many ounces of chocolate will be used in the larger cake?

(1) The original recipe calls for exactly five teaspoons of vanilla extract.

(2) If the original recipe were altered proportionally to yield a cake that serves eight people, ten teaspoons of vanilla extract would be used.

Can you tell me why I should not interpret this problem as 2X + 1X = 4
and the altered proportionality as 3X + 1.5X = 6 and then solve for X?

and instead solve for X using the statements?

Thanks for the help!
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Source: — Data Sufficiency |
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by sourabh33 » Tue May 17, 2011 9:26 pm
Given

Ratio of Chocolate to Vanilla Extract --> 1 Ounce : 2 Teaspoon
Total teaspoons of extract for serving 4 --> T
Therefor Total Chocolate in serving for 4 --> T/2

To find --> Chocolate quantity in larger cake

(This cannot be represented as 2x + x because ounce and teaspoons are different units. The equation just tells us the quantity correlation of chocolate to vanilla extract. In addition, there could be certain other ingredients that could be part of the mix apart from the chocolate and extract, and therefore we cannot represent 2x + o =4.)

Evaluating Statement 1

Teaspoons of extract in original recipe = 5
Total Chocolate in Original recipe = 5/2 = 2.5 Ounce
Chocolate per person = 2.5/4 = 0.625
Therefor Chocolate required for Larger Cake = 0.625 x 6 = 3.725

Therefore sufficient


Evaluating Statement 2
Teaspoons of extract in cake for 8 = 10
Teaspoons of extract in cake for 4 = 10/2 = 5
Total Chocolate in Original recipe = 5/2 = 2.5 Ounce
Chocolate per person = 2.5/4 = 0.625
Therefor Chocolate required for Larger Cake = 0.625 x 6 = 3.725

Therefore sufficient

Hence the answer should be D
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