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If a,b,x, and y are positive integers, is a^-x > b^-y?
(1) a < b
(2) x < y
(1) a < b
(2) x < y
Target question: Is a^(-x) > b^(-y)?alanforde800Maximus wrote:If a,b,x, and y are positive integers, is a^-x > b^-y?
(1) a < b
(2) x < 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
