Data Sufficiency

AAPL wrote:Manhattan Prep

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.

OA D

Given: Ratio vanilla extract (teaspoons) to chocolate (ounce) = 2 : 1
We have to find out how many ounces of chocolate would be needed to make a cake that serves 6 people.

Let's take each statement one by one.

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

Given that the original recipe (for 4 people) calls for exactly 5 teaspoons of vanilla extract, the larger cake (6 people) will need (5/4)*6 = 7.5 teaspoons of vanilla extract.

Since the ratio vanilla extract (teaspoons) to chocolate (ounce) = 2 : 1, the larger cake for 6 people will need 7.5/2 = 3.75 ounces of chocolate. Sufficient.

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

=> Number of teaspoons of vanilla extract needed to make the cake for 6 people = (10/8)*6 = 7.5 teaspoons of vanilla extract

Since the ratio vanilla extract (teaspoons) to chocolate (ounce) = 2 : 1, the larger cake for 6 people will need 7.5/2 = 3.75 ounces of chocolate. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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