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

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

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

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Re: Inequality [#permalink] New post 08 Sep 2010, 10:57
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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.

Answer: C.
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Re: Inequality [#permalink] New post 08 Sep 2010, 12:11
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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] New post 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.

Answer: C.


Bunuel,
Can you explain how it reduce it to |x| from the expression?
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Re: Inequality [#permalink] New post 09 Sep 2010, 09:12
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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.

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;

So -1<x<1.
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Re: absolute value [#permalink] New post 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

Answer is (c)
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Re: Inequality [#permalink] New post 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 :P

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Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink] New post 04 Jul 2013, 00:24
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Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink] New post 04 Jul 2013, 06:12
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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] New post 04 Jul 2013, 11:15
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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] New post 24 Sep 2013, 00:22
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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] New post 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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If x#0, is |x|/x<1? (1) x < 1 (2) x > −1 [#permalink] New post 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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