Let's understand |x| > 1. For |x| > 1 to be true, x can be any integer other than -1, 0 and 1.VJesus12 wrote:If x is an integer, is |x| > 1?
(1) (1 - 2x)(1 + x) < 0
(2) (1 - x)(1 + 2x) < 0
[spoiler]OA=C[/spoiler]
Source: GMAT Club Tests
So, the question is whether x is one among -1, 0 and 1.
Let's take each statement one by one.
(1) (1 - 2x)(1 + x) < 0
Case 1: Say x = 1
At x = 1, we have (1 - 2x)(1 + x) < 0 => (1 - 2*1)(1 + 1) < 0 => -2 < 0. Valid result. The answer is no since x is one among -1, 0 and 1.
Case 2: Say x = 2
At x = 2, we have (1 - 2x)(1 + x) < 0 => (1 - 2*2)(1 + 2) < 0 => -6 < 0. Valid result. The answer is yes since x is not one among -1, 0 and 1.
Insufficient.
(2) (1 - x)(1 + 2x) < 0
Case 1: Say x = -1
At x = -1, we have (1 - x)(1 + 2x) < 0 => (1 + 1)(1 + 2*-1) < 0 => 2*(1 - 2) < 0 => -2 < 0. Valid result. The answer is no since x is one among -1, 0 and 1.
Case 2: Say x = 2
At x = 2, we have (1 - x)(1 + 2x) < 0 => (1 - x)(1 + 2x) < 0 => (1 - 2)(1 + 2*2) => -5 < 0. Valid result. The answer is yes since x is not one among -1, 0 and 1.
Insufficient
(1) and (2) together
We see that among three values of x (1, 0 and -1), only x = 1 qualify for Statement 1 and only x = -1 qualify for Statement 2; thus, none of x (1, 0 and -1) qualifies for both the statements. Thus, the answer is Yes. Sufficient.
The correct answer: C
Hope this helps!
-Jay
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