Data Sufficiency

VJesus12 wrote:Is A^B > B^A?

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

The OA is the option E.

Experts, can you help me to solve this DS queston? I don't know how to start it?

We have to determine whether A^B > B^A.

(1) A^A > A^B

Case 1: Say A = 3 and B = 1, then A^A = 3^3 = 9 and A^B = 3^1 = 3, we see that 9 > 3 or A^A > A^B

Let' see the question inequality A^B > B^A. At such values, B^A = 1^3 = 1

We see that A^B (= 3) > B^A (1). The answer is Yes.

Case 2: Say A = -2 and B = 1, then A^A = -2^(-2) = 1/(-2^2) = 1/4 and A^B = -2^1 = -2, we see that 1/4 > -2 or A^A > A^B

Let' see the question inequality A^B > B^A. At such values, B^A = 1^(-2) = 1

We see that A^B (= -2) < B^A (1). The answer is No. Insufficient.

(2) B^A > B^B

On the basis of Statement 1, we can conclude that Statement 2 would also be insufficient.

(1) and (2) together

We have A^A > A^B form St 1 and B^A > B^B from St 2.

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

Dividing equation (1) by equation (2), we get

A^A / B^A > A^B / B^B

(A/B)^A > (A/B)^B

=> (A/B)^(A - B) > 1

This is possible if either A = B or A - B = 1

Case 1: If A = B, then the question inequality A^B > B^A => A^A = A^A. The answer is No.

Case 2: If A - B = 1; say A = 2 and B =1, then the question inequality A^B > B^A => 2^1 > 1^2. The answer is Yes.

Insufficient.

The correct answer: E

Hope this helps!

-Jay
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