A certain mixture of paint requires blue, yellow,

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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.

Official Guide question
Answer: C

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by Brent@GMATPrepNow » Mon Jul 24, 2017 10:04 am
jjjinapinch 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.

Official Guide question
Answer: 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

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Brent
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by Jay@ManhattanReview » Mon Jul 24, 2017 9:57 pm
jjjinapinch 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.

Official Guide question
Answer: C
We have to find out whether there enough of the yellow paint to make the desired amount of the mixture.

Statement 1: Exactly 20 quarts of the mixture are needed.

As per the given ratio, 2 : 3 : 1, we would need [3 / (2+3+1)]*20 = (3/6)*20 = 10 quarts of yellow paint

However, we do not know how much yellow paint is available. Insufficient.

Statement 2: Exactly 10 quarts of the yellow paint are available.

We do not know how much mixture is needed. If the quantity of the mixture is such that the required quantity of yellow paint is less than equal to 10 quarts, then the answer is Yes. However, if the quantity of the mixture is such that the required quantity of yellow paint is more than 10 quarts, then the answer is No. Insufficient.

Statement 1 & 2:

From both the statements, we get to know that we need 10 quarts of yellow paint, and it is available, thus both the statement together are sufficient.

The correct answer: C

Hope this helps!

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by Scott@TargetTestPrep » Thu Nov 16, 2017 7:17 am
jjjinapinch 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.
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

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