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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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