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Director  V
Joined: 12 Feb 2015
Posts: 862

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Difficulty:   35% (medium)

Question Stats: 69% (01:30) correct 31% (01:25) wrong based on 98 sessions

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Is x positive?

(1) |x + 6| > 6

(2) |x - 6| > 6

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Manish "Only I can change my life. No one can do it for me"
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Joined: 12 Sep 2015
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CAMANISHPARMAR wrote:
Is x positive?

(1) |x + 6| > 6

(2) |x - 6| > 6

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k

Note: these rules assume that k is positive

Target question: Is x positive?

Statement 1: |x + 6| > 6
Applying Rule #2, we can conclude that EITHER x + 6 > 6 OR x + 6 < -6
Let's examine each possible case:
Case a: If x + 6 > 6, then we can subtract 6 from both side to get x > 0. In this case, the answer to the target question is YES, x IS positive
Case b: If x + 6 < -6, then we can subtract 6 from both side to get x < -12. In this case, the answer to the target question is NO, x is NOT positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x - 6| > 6
Applying Rule #2, we can conclude that EITHER x - 6 > 6 OR x - 6 < -6
Let's examine each possible case:
Case a: If x - 6 > 6, then we can add 6 to both side to get x > 12. In this case, the answer to the target question is YES, x IS positive
Case b: If x - 6 < -6, then we can add 6 to both side to get x < 0. In this case, the answer to the target question is NO, x is NOT positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 indirectly tells us that EITHER x > 0 OR x < -12
Statement 2 indirectly tells us that EITHER x > 12 OR x < 0
Since both statements are true, we should look for values of x that satisfy BOTH statements.
There are several values of x that satisfy BOTH statements. Here are two:
Case a: x = 15. In this case, the answer to the target question is YES, x IS positive
Case b: x = -15. In this case, the answer to the target question is NO, x is NOT positive
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
_________________ Re: Is x positive?   [#permalink] 13 Jan 2019, 11:55
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