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If wxy ≠ 0, does x = y?

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If wxy ≠ 0, does x = y?

by M7MBA » Wed May 23, 2018 5:00 am

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If wxy ≠ 0, does x = y?

(1) w^x = w^y

(2) wxy ≠ xy

The OA is the option E.

Why is the first statement not sufficient? Actually, I would like to know why is E the correct answer. Could someone give me an explanation here? Please.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed May 23, 2018 5:48 am

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M7MBA wrote:If wxy ≠ 0, does x = y?

(1) w^x = w^y
(2) wxy ≠ xy
Target question: Does x = y?

Given: wxy ≠ 0

IMPORTANT: When I scan the two statements, I can see that this question is testing us on our knowledge about when we can conclude that two exponents are equal.
For statement 1, many students will conclude that, if w^x = w^y, then it must be true that x = y.
HOWEVER, this is true only if w does NOT equal 0, 1 or -1
For example, if 1^x = 1^y, we can't then conclude that x = y
Given all of this, we can jump straight to .....

Statements 1 and 2 combined
There are many values of w, x and y that satisfy BOTH statements. Here are two:
Case a: w = -1, x = 2 and y = 2. These values work because (-1)^2 = (-1)^2. In this case, the answer to the target question is YES, x = y
Case b: w = -1, x = 2 and y = 4. These values work because (-1)^2 = (-1)^4. In this case, the answer to the target question is NO, x does NOT equal y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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