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.
Is A^B > B^A?
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(1) A^A > A^BVJesus12 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.
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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