Inequality question...tough one

I'm getting B

1) Is insufficient because x could be positive and X / [x] could be 1 which
would be less than x. Example 5 / 5 < 5. X could also be negative
- x / x < x or -5 / 5 <5> x. x would have to be negative for that to be true.

what does everyone else get.

is it B..??

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

(2) The second statement says that |x| > x . The only way for this to be true is for x to be a negative number. But how do you know from this statement that x=-0.5 or -3. x= -0.5 means that |x|=0.5 which is less than 1 but if x=-3 then |x|=3 which is greater than 1. So (2) is insufficient. The answer here is maybe not a difinite yes or no.

(1) x/|x| < x well this is telling us that if x = -3 then |x| = 3 x/|x| = -1 in this case which not < -3. Or if x = 5, |x| = 5 then x/|x|=1 which is < 5 so (1) is also insufficient. Again a maybe not a difinite yes or no.

Now (1) and (2) together. (2) tells us that x has to be a negative number, though the actual value of x is unknown. Using statement (2) into (1) for any negative x such as -5, |x| = 5 then x/|x|=-1. -1 is greater than -5. Try again for x=-0.25 |x|=0.25 x/|x|=-1 in this case but -1 is less than -0.25. Sadly a maybe because there are many different values that answers this statement and there are many values that does not.

In conclusion after all of this trial and error we know that (1) and (2) together is still insuffienct to get a definate yes/no.

I would answer (E)

Hope that is correct, otherwise I just wasted 5 minutes of my time.

Cheers and wish me luck people, I have got only one week to go till the big day.
Kaunteya

Kaunteye i think u r right.The ans should be E.

Someone refered this questtion to me ....according to that person the OA is C.I just needed to confirm it.

Thanks guys for all the help.

The QA should be C

Statement 2 tells us it's negative.

For statement 1 to be true, X must be a fraction.

If X = -1/2

-1/2 / 1/2 = -1 < -1/2 --> True


If X = -3

-3/3 = -1 > -3 --> False