Shalabh's Quants wrote:aneesh.kg wrote:Hi,
I am totally on your side.
The question is NOT asking us the complete solution of x, but is only asking which of the values of x among the options will satisfy the inequality.
Here goes my solution:
x/|x| < x
Multiplying both sides by |x|, we have
x < x.|x|
x(|x| - 1) > 0
I)
When
x > 0, |x| = x and
x(x - 1) > 0
Using Critical Points' method,
x > 1
So, [spoiler](A)[/spoiler] is correct. We don't need to go further. The next case is of x < 0 so x > 1 will always satisfy the given inequality.
But we will, for the sake of more analysis.
(
B) cannot be correct; x = 1/2 does not satisfy the inequality.
----------------------------------------
II)
When
x < 0, |x| = -x
x(-x - 1) > 0
x(x + 1) < 0
Using Critical Points' method,
-1 < x < 0
Combining I) and II),
-1 < x < 0 OR x > 1
What is the Critical Points' method?
Read here:
https://www.beatthegmat.com/critical-poi ... 10450.html
Dear Aneesh,
This is a
Must Be True kind of question. Agreed that Inequality does not satisfy for X being between 0 & 1.
Imagine 2 scenarios...
Scenarios 1:- X is say 3, Inequality satisfies, and options A & B both satisfy.
Scenarios 2:- X is say -1/2, option B satisfies, option A does not.
So we cannot necessarily state that X > 1 only, whereas we can necessarily state that X > -1. I think Answer is
B.
Can we have your opinion Mitch?
Correct.
If x>1, then it must be true that x/|x| < x.
But the question here is the reverse:
If x/|x| < x, then what must be true about x?
Since any value between -1 and 0 satisfies x/|x| < x, we cannot say that it must be true that x > 1.
Hence, we can eliminate A (and any other answer choice that does not include -1<x<0 within its range).
What must be true about x is that x > -1, since no value less than or equal to -1 satisfies x/|x| < x.
Hence, the correct answer is
B.
Last edited by
GMATGuruNY on Thu May 19, 2016 12:57 pm, edited 1 time in total.
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