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1. if you set x= positive decimal you get the original value which is <1 now you can try x = negative integer(-5) which results in the positive version which is >1 so INSUFF 2. this is INSUFF since x could be a huge positive number which makes it >1 OR it could be a small decimal number which makes it <1
combining you see -1< X <1 which means X is a +/- decimal which also means it will be <1 so C _________________
If \(x\neq{0}\), is \(\frac{x^2}{|x|}<1\)? --> reduce by \(|x|\) --> is \(|x|<1\)? or is \(-1<x<1\)?
Two statements together give us the sufficient info.
Answer: C.
Bunuel, Can you explain how it reduce it to \(|x|\) from the expression?
Given: \(\frac{x^2}{|x|}<1\)
Consider this: \(\frac{x^2}{|x|}=\frac{|x|*|x|}{|x|}=|x|\). It's basically the same as if it were \(\frac{x^2}{x}\) --> we could reduce this fraction by \(x\) and we would get \(x\), and when \(x\) is positive, result is positive and when \(x\) is negative, result is negative. Now, \(\frac{x^2}{|x|}\) is the ratio of two positive values and the result can not be negative, so we can not get \(x\), we should get \(|x|\) to guarantee that the result is positive.
OR: \(x<0\)--> then \(|x|=-x\) --> \(\frac{x^2}{|x|}=\frac{x^2}{-x}=-x<1\) --> \(x>-1\);
\(x>0\)--> then \(|x|=x\) --> \(\frac{x^2}{|x|}=\frac{x^2}{x}=x<1\);
Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink]
04 Jul 2013, 06:12
1
This post received KUDOS
\(x^2/|x|\) reduces to |x||x|/|x| which reduces the qn to is |x| <1 ? This again reduces to -1< x <1. Only combining (1) and two answers this qn. Hence answer is (C).
Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink]
24 Sep 2013, 00:38
Expert's post
stne wrote:
udaymathapati wrote:
If x#0, is |x|/x<1?
(1) x < 1 (2) x > −1
I think\(\frac{|x|}{x} <1\)
(1) x < 1 (2) x > −1
Here the answer should be E
x= 1/2 satisfies both the statements and answer to the stem is no, 1 is not less 1
X= - 1/2 satisfies both the statements and answer to the stem is yes , -1<1
but for question \(\frac{x^2}{x} <1\)
(1) x < 1 (2) x > −1
here the answer is C as shown above
Please do correct if I am missing something thanks.
If it were: If x#0, is |x|/x<1?
(1) x < 1 (2) x > −1
Then the answer is E. The question basically asks whether x is negative and we cannot answer that even when we combine the statements given.
If it were: If x#0, is x^2/x<1?
(1) x < 1 (2) x > −1
Then the answer is C. The question basically asks whether x<0 or 0<x<1. When we combine the statements, we get that -1<x<1 (x#0). So, the answer to the question is YES. _________________
Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink]
24 Sep 2013, 01:35
Bunuel wrote:
stne wrote:
udaymathapati wrote:
If x#0, is |x|/x<1?
(1) x < 1 (2) x > −1
I think\(\frac{|x|}{x} <1\)
(1) x < 1 (2) x > −1
Here the answer should be E
x= 1/2 satisfies both the statements and answer to the stem is no, 1 is not less 1
X= - 1/2 satisfies both the statements and answer to the stem is yes , -1<1
but for question \(\frac{x^2}{x} <1\)
(1) x < 1 (2) x > −1
here the answer is C as shown above
Please do correct if I am missing something thanks.
If it were: If x#0, is |x|/x<1?
(1) x < 1 (2) x > −1
Then the answer is E. The question basically asks whether x is negative and we cannot answer that even when we combine the statements given.
If it were: If x#0, is x^2/x<1?
(1) x < 1 (2) x > −1
Then the answer is C. The question basically asks whether x<0 or 0<x<1. When we combine the statements, we get that -1<x<1 (x#0). So, the answer to the question is YES.
as you can see the question has now been corrected
originally udaymathapati had changed x^2 to |x| and posted the question
where is my kudo for pointing this out ? _________________
Re: If x#0, is x^2/|x| < 1? [#permalink]
09 Sep 2015, 06:14
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
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