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Is x > 0 ?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Oct 30, 2017 3:06 am
LUANDATO wrote:Is x > 0 ?

(1) |x+3| < 4
(2) |x-3| < 4

The OA is E.

Please, can any expert assist me with above problem? I need help to solve it. Thanks.
(1) |x+3| < 4

=> x+3 < 4 => x < 1. If 0 < x < 1, the answer is Yes.

or

=> x+3 > -4 => x > -7, the answer is No. Insufficient.

(2) |x-3| < 4

=> x - 3 < 4 => x < 7. If 0 < x < 7, the answer is Yes.

or

=> x - 3 > -4 => x > -1. If 0 > x > -1, the answer is No. Insufficient.

(1) and (2) combined:

We have a common range -1 < x < 1 from both the statements. If -1 < x < 0, the answer is No. However, if 0 < x < 1, the answer is yes. Insufficient.

The correct answer: E

Hope this helps!

-Jay

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