DS from Mgmat

[adi_800]

If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x

[neelgandham]

If x is not equal to 0, is |x| less than 1? Is |x| < 1 => is -1 < x < 1 ?

(1) x/|x| < x

Multiply |x| to both sides as |x| > 0, we get x < x|x| => x > 1 and -1 < x <0

In sufficient

(2) |x| > x

=> x < 0

[spoiler]Insufficient.

joining the two statements, you get -1 < x < 0, which answers the question ! [/spoiler]

Hence Option C

[adi_800]

OA is not A

[neelgandham]

OA is not A

My bad! I missed a condition. I have edited the post now!

[nandy1984]

If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x

(2) |x| > x

Statement (1) x/|x| < x

X = 2 --> x/|x| < x --> TRUE --> |x| < 1 is NO
X = -1/4 ---> x/|x| < x --> -1 < -1/4 --> TRUE --> |x| < 1 is YES
So INSUFFICIENT...

Statement (2)
|x| > x

|x| is always greater than x only if x is negative which is a negative number or negative fraction

If x = -20 --> |x| > x correct and |x| < 1 is NO
If x = -1//4 --> |x| > x correct and |x| <1 is YES

So we have two answers so insufficient...

If we both combine the statements we can take x = -1/4 only which will satisfy both the statements...so answer is C.....Is this answer correct???? Plz post the answer... thanks...
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[bpdulog]

C