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# Is x= a^b>0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82

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08 Dec 2017, 00:06
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Difficulty:

15% (low)

Question Stats:

83% (00:34) correct 17% (00:05) wrong based on 42 sessions

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[GMAT math practice question]

Is $$x= a^b>0$$?

1) $$a$$ is positive
2) $$b$$ is a prime number
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Aug 2009
Posts: 5540

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08 Dec 2017, 00:31
MathRevolution wrote:
[GMAT math practice question]

Is $$x= a^b>0$$?

1) $$a$$ is positive
2) $$b$$ is a prime number

Pl correct the Question..
Most likely it should be is a^b>0..

1) a is positive..
Whatever be the value of b, a^b>0
Suff

2) b is a prime number..
If it is 2, Ans will be YES always..
Otherwise it will depend on a.
Insufficient

A
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Joined: 05 Dec 2016
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08 Dec 2017, 01:21
(1) a is positive, hence any value of b wqould give us positvie result
Sufficient
(2) b can take 2;3;7 etc
a= -1 ; b=2 then x would be +ve
a=-1 ; b=3 then x would be -ve
Insufficient

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82

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10 Dec 2017, 17:12
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA method is to modify the original condition and the question, and then recheck the question.

Condition 1)
If $$a > 0$$, then $$a^b>0$$. The answer is ‘yes’.
So, this condition is sufficient.

Condition 2)
For $$a = 2, b = 2$$, we have $$a^b = 2^2 = 4 > 0$$, and the answer is ‘no’.
For $$a = -2, b = 3$$, we have $$a^b = (-2)^2 = -8 < 0$$, and the answer is ‘yes’.
So, condition 2) is not sufficient.

Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E).

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Re: Is x= a^b>0?   [#permalink] 10 Dec 2017, 17:12
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