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Is A^B > B^A?

This topic has 1 expert reply and 0 member replies

Is A^B > B^A?

Post Wed Nov 08, 2017 7:52 am
Is A^B > B^A?

(1) A^A > A^B
(2) B^A > B^B

The OA is E.

How can I conlcude that the correct option is E? Experts, I ask for your help.

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Post Wed Nov 08, 2017 10:19 pm
VJesus12 wrote:
Is A^B > B^A?

(1) A^A > A^B
(2) B^A > B^B

The OA is E.

How can I conlcude that the correct option is E? Experts, I ask for your help.
(1) A^A > A^B

Case 1: Say A = 2 and B = 1, then A^A > A^B => 2^2 > 2^1. We see that the question inequality A^B > B^A => 2^1 > 1^2. The answer is Yes.
Case 2: Say A = 2 and B = -1, then A^A > A^B => 2^2 > 2^(-1). We see that the question inequality A^B > B^A => 2^(-1) > (-1)^2. The answer is No. No unique answer. Insufficient.

(2) B^A > B^B

Case 1: Say A = 2 and B = 1, then B^A > B^B => 1^2 > 1^1. We see that the question inequality A^B > B^A => 2^1 > 1^2. The answer is Yes.
Case 2: Say A = 2 and B = -1, then B^A > B^B => (-1)^2 > (-1)^(-1). We see that the question inequality A^B > B^A => 2^(-1) > (-1)^2. The answer is No. No unique answer. Insufficient.

(1) and (2) combined:

Both the cases discussed above are applicable to both the statements, thus, the answer is not unique. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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