Someone explain it please...

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Someone explain it please...

by akpareek » Wed Sep 04, 2013 10:36 am
If ab=1, what is the value of (axb)(ayb)?

1. ax= by= 2
2. 2xy= 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Sep 04, 2013 10:58 am
akpareek wrote:If ab = 1, what is the value of (axb)(ayb)?

1. ax = by = 2
2. 2xy = 4
Target question: What is the value of (axb)(ayb)?
This question is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

(axb)(ayb) = (ab)(ab)(xy)
= (1)(1)(xy) [since we're told that ab = 1]
= xy
Since (axb)(ayb) = xy, we can rephrase the target question. . .

Rephrased target question: What is the value of xy?

Statement 1: ax = by = 2
So, (ax)(by) = (2)(2)
Rearrange: (ab)(xy) = 4
Replace ab with 1 to get: xy = 4
Since we can answer the rephrased target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2xy = 4
So, we can see that xy = 2
Since we can answer the rephrased target question with certainty, statement 2 is SUFFICIENT

Hmmm, there's a small problem with this question. On the GMAT, the statements are assumed to be true. Statement 1 essentially tells that xy = 4, BUT statement 2 tells that xy = 2. Are you sure you wrote the question correctly?

Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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