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# If x#0, is x^2/|x| < 1?

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Manager
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If x#0, is x^2/|x| < 1? [#permalink]  08 Sep 2010, 10:51
2
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Difficulty:

45% (medium)

Question Stats:

59% (01:50) correct 41% (00:58) wrong based on 151 sessions
If x#0, is x^2/|x| < 1?

(1) x < 1
(2) x > −1
[Reveal] Spoiler: OA

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Maths1.JPG [ 2.56 KiB | Viewed 2510 times ]

Math Expert
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Re: Inequality [#permalink]  08 Sep 2010, 10:57
2
KUDOS
Expert's post
udaymathapati wrote:
[img]
Attachment:
Maths1.JPG
[/img]

(1) x < 1
(2) x > −1

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.

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Re: Inequality [#permalink]  08 Sep 2010, 12:11
1
KUDOS
udaymathapati wrote:
[img]
Attachment:
Maths1.JPG
[/img]

(1) x < 1
(2) x > −1

x^2/abs(x) <1 ?

Another way to look at it...

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
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Re: Inequality [#permalink]  09 Sep 2010, 03:38
Bunuel wrote:
udaymathapati wrote:
[img]
Attachment:
Maths1.JPG
[/img]

(1) x < 1
(2) x > −1

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.

Bunuel,
Can you explain how it reduce it to $$|x|$$ from the expression?
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Re: Inequality [#permalink]  09 Sep 2010, 09:12
1
KUDOS
Expert's post
udaymathapati wrote:
Bunuel wrote:
udaymathapati wrote:
[img]
Attachment:
Maths1.JPG
[/img]

(1) x < 1
(2) x > −1

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.

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 $$|x|=x$$ --> $$\frac{x^2}{|x|}=\frac{x^2}{x}=x<1$$;

So $$-1<x<1$$.
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Re: absolute value [#permalink]  14 Oct 2010, 13:44
tatane90 wrote:
If x ≠ 0, is x^2/|x| < 1?
(1) x < 1
(2) x > −1

$$\frac{x^2}{|x|} \lt 1$$
If x>0, then this implies x<1
If x<0, then this implies x>-1
So it is only true if either 0<x<1 or -1<x<0

(1) Not sufficient clealry, as x is not bounded on lower side
(2) Not sufficient clealrly, as x is not bounded on upper side

(1+2) Exactly defined the range for which the inequality holds. Sufficient

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Re: Inequality [#permalink]  16 Oct 2010, 03:49
Bunuel, did anybody tell you that you are a genius? Stay away from scientists, they might start researching on your brain

+1
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Ganesh
Class of 2012
Great Lakes Institute of Management
http://greatlakes.edu.in

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Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink]  04 Jul 2013, 00:24
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink]  04 Jul 2013, 06:12
1
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).
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Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink]  04 Jul 2013, 11:15
1
KUDOS
x^2/|x| < 1
(x^2 = |x|*|x|)
SO
(|x|*|x|)/|x| < 1
Is |x|<1?
is x<1 or is x>-1
is -1<x<1?

(1) x < 1
The issue here is depending on what x is, x may not be in the range of -1<x<1.
INSUFFICIENT

(2) x > −1
The same problem that applied to a) applies to b).
INSUFFICIENT

a+b) this gives us a range of -1<x<1 which is what the question is looking for.
SUFFICIENT

(C)
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Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink]  24 Sep 2013, 00:22
1
KUDOS
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.
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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.
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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 ?
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Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1   [#permalink] 24 Sep 2013, 01:35
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