ChiranjeevSingh wrote:
If a and b are integers and \(a^b<b^a<0\), which of the following statements must be true?
I. ab>0
II. b<a
III. (ab+1) is divisible by 2
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and II
I created this question today, a thing I did in a very long time. Thought of sharing the same with the vibrant GMAT Club community. I'll post the solution after some discussion on the thread. Please feel free to share your feedback on the question.
- CJ
+ stands for positive integer
- stands for negative integer
E stands for even
O stands for Odd
(a,b) can only be (-O,-O), (-E,-E), (-E,-O), (-O,-E)
by putting numbers:
Case 1 (-O, -O) = (-3, -5) or (-5, -3)
(-3,-5) does not satisfy a^b<b^a<0
(-5,-3) do satisfy the a^b<b^a<0, here ab>0, b>a, ab+1 is divisible by 2
Fight between option A & C left
Case 2 (-E, -E) = (-6,-2) or (-2,-6)
(-2,-6) does not satisfy a^b<b^a<0
(-6,-2) do satisfy the a^b<b^a<0, here ab>0, b>a, ab+1 is not divisible by 2
Only option left is A
Please correct me if i am wrong (Noob).
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