Deepthi Subbu wrote:If x is not equal to 0, is |x| less than 1?
(1)x/|x| < x
(2) |x| > x
Question rephrased: Is x a positive or negative fraction?
Plug in the following:
One positive fraction
One positive integer greater than 1
One negative fraction
One negative integer less than -1.
Statement 1: x/|x| < x.
x = 1/2 does not work.
x = 2 works.
x = -1/2 works.
x = -2 does not work.
Since x = -1/2 is between -1 and 1 and x=2 is not, INSUFFICIENT.
Statement 2: |x| > x
x = 1/2 does not work.
x = 2 does not work.
x = -1/2 works.
x = -2 works.
Since x = -1/2 is between -1 and 1 and x=-2 is not, INSUFFICIENT.
Statements 1 and 2 combined:
Only x = -1/2 satisfies both statements.
It is not possible in statement 1 that x=1 or that x=-1.
Thus, we know that x must be a negative fraction.
SUFFICIENT.
The correct answer is
C.
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