Is x negative? (1) |1 - x| 1

Question

Is x negative?

(1) |1 - x| < 1
(2) |1 + x| > 1

Bounce1987 · Answer

if x>0 or x<2 then since x<2 it can be negative also? first statement gives x>0 or x<2. How is A sufficient?

Bunuel · Answer

x > 0 and x < 2 are simultaneous conditions, so you should consider them together as 0 < x < 2. |1 - x| < 1 -1 < 1 - x < 1 Subtract 1 from all three parts: -2 < -x < 0. Multiply by -1 and flip the signs as we multiply by negative number: 2 > x > 0.

Bunuel · Answer

Is x negative? (1) |1−x| < 1 . From this, we can infer that -1 < 1-x < 1 . Subtracting 1 from all parts, we get: -2 < -x < 0 . Multiplying everything by -1, we have: 2 > x > 0 . This indicates x is positive. Sufficient. (2) |1+x| > 1 . From this, we can infer that 1 + x < -1 or 1 + x > 1 . Hence, x < -2 or x > 0 . Thus, x could either be positive or negative. Not sufficient. Answer: A

Is x negative? (1) |1 - x| < 1 (2) |1 + x| > 1

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