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Is 3^(a^2/b) < 1?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Dec 04, 2017 9:35 pm
M7MBA wrote:Is 3^(a^2/b) < 1?

(1) a<0

(2) b<0

The OA is C .

Experts, what is the best way to solve this DS question? Can you help me?
For 3^(a^2/b) to be less than 1, note that a^2/b must be less than 0. Since a^2 is always a non-negative number, it can be 0 or a positive number. But a must not be 0 since at a = 0, the power a^2/b would be 0 and 3^0 would be 1 (Not less than 1).

So, we need to see two conditions: 1. a ≠ 0 and 2. b must be negative.

(1) a<0

Insufficient. We do not know whether b is negative.

(2) b<0

Insufficient. We do not know whether a is not 0.

(1) and (2) together

Sufficient.

The correct answer: C

Hope this helps!

-Jay
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