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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
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    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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