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DS : Is X^(a+b) > X^(a-b)

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Source: — Data Sufficiency |

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by [email protected] » Thu Jun 04, 2015 9:37 am
Hi nikhilgmat31,

We're told that A and B are POSITIVE INTEGERS. We're asked if X^(A+B) > X^(A-B). This is a YES/NO question.

Before dealing with the two Facts, it's worth spending a few moments to look at the 'design' of the question...

Since A and B are both POSITIVE INTEGERS, (A+B) will ALWAYS be greater than (A-B). So the answer to this question is going to come down to the value of X.....

Fact 1: X(A+1) > X(A-1)

IF...
X = 1, (A+1) is > (A-1)
1^(A+B) = 1^(A-B), so the answer to the question is NO

IF...
X = 2, (2A+2) > (2A-2)
2^(A+B) > 2^(A-B), so the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: A = B+2

This tells us NOTHING about the value of X, so X can be 1 (the answer is NO) or 2 (the answer is YES).
Fact 2 is SUFFICIENT

Combined, we already know that X can be 1 or 2 and that each of those results has different answers...
Combined, INSUFFICIENT

Final Answer: E

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by nikhilgmat31 » Fri Jun 05, 2015 1:19 am
I also thought E But in case # 1

X^a * X > X^a / X

Considering X as positive & >1 , Cancelling X^a
X > 1/X

X^2 >1
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by [email protected] » Fri Jun 05, 2015 9:30 am
HI nikhilgmat31,

Currently, in Fact 1, it appears that we're dealing with MULTIPLICATION and NOT EXPONENTS. If Fact 1 is not written correctly (and it's meant to state something else), then the answer to the question could change.

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by nikhilgmat31 » Sun Jun 07, 2015 11:01 pm
I also thought E But in case # 1

X^a * X > X^a / X

Considering X as positive & >1 , Cancelling X^a
X > 1/X

X^2 >1

But this yields to X can be +ive or -ive .. so OA is E
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