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DS - Average Problem

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Source: — Data Sufficiency |
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by buzzdeepak » Mon Dec 24, 2012 5:41 am
Question is: Are we supposed to look at both the options and see if we are able to find the solution individually as well together?

In this case, 1 gives us a solution right away, but 2 needs 1 to get to the solution.

So, A or C?

Thanks...
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by Brent@GMATPrepNow » Mon Dec 24, 2012 7:50 am
buzzdeepak wrote:What is the average of x and Y?
1. x+y=20
2. 2x+4y=54
Target question: What is the average of x and Y?

Since the average (mean) of x and y is equal to (x+y)/2, we can rephrase the target question to get...

Rephrased target question: What is the value of (x+y)/2?

Statement 1: x+y=20
If x+y=20, then (x+y)/2 = 20/2 = 10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2x+4y=54
There are several pairs of values for x and y that meet this condition. Here are two:
Case a: x=27, y=0, in which case (x+y)/2 = 27/2 = 13.5
Case b: x=15, y=6, in which case (x+y)/2 = 21/2 = 10.5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Brent
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by Brent@GMATPrepNow » Mon Dec 24, 2012 7:54 am
buzzdeepak wrote:Question is: Are we supposed to look at both the options and see if we are able to find the solution individually as well together?

In this case, 1 gives us a solution right away, but 2 needs 1 to get to the solution.

So, A or C?

Thanks...
Always begin by examining each statement by itself. If neither statement alone is sufficient, then you can check whether the combined statements are sufficient.

Also, keep in mind what each answer choice means:

A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

D: EACH statement ALONE is sufficient to answer the question asked.

E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Answer choice C says that "NEITHER statement ALONE is sufficient to answer the question asked." Since statement (1) alone is sufficient, the correct answer cannot be C.

Cheers,
Brent
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by buzzdeepak » Mon Dec 24, 2012 8:11 am
Thanks for the detailed explanation, Brent. It's crystal clear now.
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