If a,b,x, and y are positive integers, is a^-x > b^-y? (

[alanforde800Maximus]

If a,b,x, and y are positive integers, is a^-x > b^-y?

(1) a < b
(2) x < y

[Brent@GMATPrepNow]

If a,b,x, and y are positive integers, is a^-x > b^-y?

(1) a < b
(2) x < y

Target question: Is a^(-x) > b^(-y)?
This is a great candidate for rephrasing the target question.

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
First recognize the following: a^(-x) = 1/(a^x) and b^(-y) = 1/(b^y)
So, we can ask Is 1/(a^x) > 1/(b^y)?
Also, since a and b are POSITIVE, we can be certain that (a^x) is POSITIVE and (b^y) is POSITIVE
So, we can safely take the inequality 1/(a^x) > 1/(b^y) and multiply both sides by (a^x) to get: 1 > (a^x)/(b^y)
Next, we can multiply both sides by (b^y) to get: (b^y) > (a^x)
So, we can now ask...
REPHRASED target question: Is (b^y) > (a^x)?

Statement 1: a < b
No information about x or y.
So, statement 1 is NOT SUFFICIENT

Statement 2: x < y
No information about a or b.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
The key here is that all 4 variables are positive.
If b is greater than a AND y is greater than x, we can be certain that (b^y) > (a^x)
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

[Scott@TargetTestPrep]

If a,b,x, and y are positive integers, is a^-x > b^-y?

(1) a < b
(2) x < y

Rephrasing the question we have:

Is 1/a^x > 1/b^y ?

Is b^y > a^x ?

Statement One Alone:

a < b

Since we do now know anything about x and y, statement one alone is not sufficient to answer the question.

Statement Two Alone:

x < y

Since we do now know anything about a and b, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Since b is greater than a, and y is greater than x, we know that b^y is greater than a^x.

Answer: C