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Is x > y ?

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Is x > y ?

by M7MBA » Mon Feb 26, 2018 1:48 am
Is x > y ?

(1) ax > ay
(2) (a^2)*x > (a^2)*y

The OA is option B.

Is sufficient the statement (2)? Experts, can you help me here? Why is not sufficient the statement (1)?
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by Jay@ManhattanReview » Mon Feb 26, 2018 5:43 am
M7MBA wrote:Is x > y ?

(1) ax > ay
(2) (a^2)*x > (a^2)*y

The OA is option B.

Is sufficient the statement (2)? Experts, can you help me here? Why is not sufficient the statement (1)?
We have to determine whether x > y.

(1) ax > ay

=> none of x, y, and a is 0.

Case 1: Say a = +1, then we have x > y. The answer is No.

Case 2: Say a = -1, then we have -x > -y
Multiplying the inequaity with -1, we have x < y. Note the reversal of sign of inquality. The answer is No.

No unique answer. Insufficient

(2) (a^2)*x > (a^2)*y

Since irrespective of the sign of a, the value of a^2 is positive, thus, we can cancel a^2 from both the sides withougt changing the sign of inquality.

Thus, (a^2)*x > (a^2)*y => x > y. The answer is Yes. Sufficient

The correct answer: B

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Mon Feb 26, 2018 9:24 am
M7MBA wrote:Is x > y ?

(1) ax > ay
(2) (a²)x > (a²)y
Target question: Is x > y ?

Statement 1: ax > ay
WARNING: Some students will divide both sides by a and incorrectly conclude that x > y.
However, before we divide by a variable, we must ensure that the variable is EITHER positive OR negative, because if we divide by a negative value, we must reverse the direction of the inequality, and if we divide by a positive value, the direction of the inequality stays the same. As it stands, we don't know whether a is positive or negative.

To see what I mean, consider these values of a, x and y that satisfy the given condition:
Case a: a = 1, x = 3 and y = 2, in which case x > y
Case b: a = -1, x = 2 and y = 3, in which case x < y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (a²)x > (a²)y
First of all, we can conclude that a DOES NOT equal 0, since the inequality wouldn't hold up.
This means that a² is a POSITIVE number.
So, we can safely divide both sides of the inequality by a² to get: x > y
So, the answer to the target question is YES, x IS greater than y
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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