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Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4

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Source: — Data Sufficiency |

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by [email protected] » Mon Sep 26, 2016 7:14 pm
Hi alanforde800Maximus,

This question can be solved by TESTing VALUES. We're asked if X > 0. This is a YES/NO question.

1) |X+3| < 4

IF....
X = 0 then the answer to the question is NO.
X = 1/2 then the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) |X-3| < 4

IF....
X = 0 then the answer to the question is NO.
X = 1/2 then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we can see that both 0 and 1/2 'fit' both Facts, but they provide different answers (a NO and a YES).
Combined, INSUFFICIENT

Final Answer: E

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Rich
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by Jay@ManhattanReview » Mon Dec 19, 2016 4:58 am
alanforde800Maximus wrote:Is x > 0 ?

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

Please assist with above problem
Let us find the range for each inequality one by one.

S1: |x+3| < 4 => x+3 < 4 => x < 1 OR |x+3| < 4 => x + 3 > -4 [pay attention to the sign change] => x > -7

=> -7 < x < 1 => For the range 0 < x < 1, the answer is YES, but for the range -7 < x < 0, the answer is NO. No unique answer!

S2: |x-3| < 4 => x-3 < 4 => x < 7 OR |x-3| < 4 => x - 3 > -4 [pay attention to the sign change] => x > -1

=> -1 < x < 7 => For the range 0 < x < 7, the answer is YES, but for the range -1 < x < 0, the answer is NO. No unique answer!

S1 & S2: After combining both the statements, the range for x is -1 < x < 1. For the range 0 < x < 1, the answer is YES, but for the range -1 < x < 0, the answer is NO. No unique answer!

OA: E

-Jay

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