Data Sufficiency

AbeNeedsAnswers wrote:A certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients. If there are ample quantities of the blue and red paints available, is there enough of the yellow paint to make the desired amount of the mixture?

(1) Exactly 20 quarts of the mixture are needed.
(2) Exactly 10 quarts of the yellow paint are available.

C

Target question: Is there enough of the yellow paint to make the desired amount of the mixture?

Statement 1: Exactly 20 quarts of the mixture are needed.
Since the ratio of blue : yellow : red = 2 : 3 : 1, we can conclude that we need:
20/3 quarts of blue paint
10 quarts of yellow paint
20/6 quarts of red paint
Since we don't know how much yellow paint is available, we cannot answer the target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: Exactly 10 quarts of the yellow paint are available.
In this case, we don't know the VOLUME of mixed paint are needed. Consider these two cases:
Case a: we need 6 quarts of the mixed paint, which means we need 2 quarts of blue paint, 3 quarts of yellow paint and 1 quarts of red paint. In this case, there IS enough yellow paint
Case b: we need 600 quarts of the mixed paint, which means we need 200 quarts of blue paint, 300 quarts of yellow paint and 100 quarts of red paint. In this case, there is NOT enough yellow paint
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that we NEED 10 quarts of yellow paint
Statement 2 tells us that we HAVE 20 quarts of yellow paint
So, YES, there IS enough yellow paint
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

Hi All,

We're told that a certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients - and that there are ample quantities of the blue and red paints available. We're asked if there is enough of the yellow paint to make the desired amount of the mixture. This is a YES/NO question.

To start, when dealing with ratio questions, it's important to recognize the 'relationships' among the items in the ratio. Here, with a ratio of 2:3:1, we know that for every 2 quarts of blue, we would need 3 quarts of yellow and 1 quart of red. Often, ratios are based on integers (for example, you can't have a 'fraction' of a person); here though, 'fractional' amounts ARE possible as long as the ratio is maintained.

1) Exactly 20 quarts of the mixture are needed.

With the information in Fact 1, we CAN determine exactly how much of each paint is required (and since yellow paint represents 3 out of every 6 'parts' of the ratio, we know that a 20 quart mixture would require 10 quarts of yellow paint). However, we don't have enough information to answer the question that is ASKED.
Fact 1 is INSUFFICIENT

2) Exactly 10 quarts of the yellow paint are available.

Fact 2 tells us how much yellow paint is available, but not how much is actually NEEDED.
Fact 2 is INSUFFICIENT

Combined, we know:
-The amount of yellow paint that is needed (10 quarts)
-The amount of yellow paint that is available (10 quarts)
Thus, we CAN answer the question - and it is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers wrote:A certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients. If there are ample quantities of the blue and red paints available, is there enough of the yellow paint to make the desired amount of the mixture?

(1) Exactly 20 quarts of the mixture are needed.
(2) Exactly 10 quarts of the yellow paint are available.

C

We are given the ratio:

blue : yellow : red = 2x : 3x : x

We need to determine if there is enough yellow paint available to allow the ratio to hold true.

Statement One Alone:

Exactly 20 quarts of the mixture are needed.

We can create the following equation:

2x + 3x + x = 20

6x = 20

x = 20/6 = 10/3

Thus, we see that 3 x 10/3 = 10 quarts of yellow paint are needed. However, since we do not know how much yellow paint is available, statement one alone is not sufficient to answer the question.

Statement Two Alone:

Exactly 10 quarts of the yellow paint are available.

Since we do not know how many quarts of paint are needed, we cannot answer the question. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using both statements together, we see that we need 10 quarts of yellow paint and we have exactly 10 quarts of yellow paint available. Thus, we have enough yellow paint.

Answer: C