Quote:
If \(x\neq{0}\) and \(\frac{x}{|x|}<x\), which of the following must be true?
(A) \(x>1\)
(B) \(x>-1\)
(C) \(|x|<1\)
(D) \(|x|>1\)
(E) \(-1<x<0\)
Hi Karishma
Can you pls help me with the answer to the above link.
I was able to solve the inequality
My answer after solving inequality is -1<x<0 or x>1
So how can be the answer not E
The point of elimination for option e in the official explanation is as given below:-How can x be 2 when the range is less than 0......
E. −1<x<0. Not necessarily true since x could be 2.
A 'must be true' question! They are absolutely straight forward if you get the fundamental but they can drive you crazy if you don't.
"My answer after solving inequality is -1<x<0 or x>1" Perfect. That is the range of x for which the inequality works. So tell me, what values can x take?
-1/2, -1/3, -2/3, 1.4, 2, 500, 123498 etc...
Now the question is "which of the following must be true?"
(A) \(x>1\)
Are all these values greater than 1? No.
(B) \(x>-1\)
Are all these values greater than -1? Yes. The answer. Note that you dont have to establish that all value greater than -1 should work for the inequality. You only have to establish that all values which work for the inequality must satisfy this condition.
(C) \(|x|<1\)
Not true for all values of x.
(D) \(|x|>1\)
Not true for all values of x.
(E) \(-1<x<0\)
Not true for all values of x.
x can take values 1.4, 2, 500 etc
I wrote a post on this beautiful question sometime back:
http://www.veritasprep.com/blog/2012/07 ... -and-sets/ _________________
Karishma
Veritas Prep GMAT Instructor
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