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

Oldest

Best Reply

Author

Message

TAGS:

Manager

Joined: 17 Aug 2009

Posts: 241

Followers: 2

Kudos [?]: 61 [0], given: 25

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

14 Dec 2009, 01:03

00:00

Question Stats:

45% (01:27) correct

54% (00:31) wrong

based on 5 sessions

If x ≠ 0, is x^2 / |x| < 1?

(1) x < 1
(2) x > −1

[Reveal] Spoiler: OA

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11594

Followers: 1799

Kudos [?]: 9583 [0], given: 826

Re: Modulus question from GMAT tests [#permalink]

14 Dec 2009, 01:47

zaarathelab wrote:

If x ≠ 0, is x^2 / |x| < 1?
(1) x < 1
(2) x > −1

We can safely reduce LHS of inequality \frac{x^2}{|x|}<1 by |x|. We'll get: is |x|<1? Basically question asks whether x is in the range -1<x<1.

Statements 1 and 2 are not sufficient, but together they are defining the range for x as -1<x<1.

Answer: C.
_________________

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

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. NEW!!!

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. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Manager

Joined: 09 May 2009

Posts: 213

Followers: 1

Kudos [?]: 45 [0], given: 13

Re: Modulus question from GMAT tests [#permalink]

14 Dec 2009, 09:22

IMO c

the expression x^2/lxl<1 will always be +ve as the N is a sqaure and mod x is always +ve

the expression is true only for fractional value

s1) tells us that x can be a +ve or -ve fractional and also can be a -int hence insuff.
s2) tells us that x can be a +ve or -ve fractional and also can be a +int hence insuff....

combinig x is only a fraction and hence suff...
_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Senior Manager

Joined: 16 Apr 2009

Posts: 349

Followers: 1

Kudos [?]: 25 [0], given: 10

Re: Modulus question from GMAT tests [#permalink]

16 Dec 2009, 20:57

Bunuel wrote:

zaarathelab wrote:

If x ≠ 0, is x^2 / |x| < 1?
(1) x < 1
(2) x > −1

We can safely reduce inequality \frac{x^2}{|x|}<1 by |x|. We'll get: is |x|<1? Basically question asks whether x is in the range -1<x<1.

Statements 1 and 2 are not sufficient, but together they are defining the range for x as -1<x<1.

Answer: C.

Bunuel - please clarify this divison -\frac{x^2}{|x|}<1 by |x|. We'll get: is |x|<1? can be done because |x| is always +ve or is there are any other reason ?
_________________

Always tag your question

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11594

Followers: 1799

Kudos [?]: 9583 [0], given: 826

Re: Modulus question from GMAT tests [#permalink]

17 Dec 2009, 04:04

ichha148 wrote:

Bunuel - please clarify this divison -\frac{x^2}{|x|}<1 by |x|. We'll get: is |x|<1? can be done because |x| is always +ve or is there are any other reason ?

We should never multiply (or reduce) inequality by variable (or expression with variable) if we don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero.

But in this case we are not reducing the inequality we are reducing only one part of it. So, it's safe to do so.

For example if we had: \frac{x^4}{x^3}<0 we can reduce LHS by x^3 and write x<0.
_________________

Senior Manager

Joined: 18 Aug 2009

Posts: 340

Followers: 5

Kudos [?]: 120 [0], given: 13

Re: Mod [#permalink]

29 Dec 2009, 06:10

If x ≠ 0, is x^2/|x|< 1?

1: x<1 - Insufficient. x can be -2 or 1/2
2:x>-1 - Insufficient. x can be 2 or 1/2

Together, sufficient. x must be a fraction, and thus the answer is C.

Intern

Joined: 21 Jul 2012

Posts: 11

Followers: 0

Kudos [?]: 0 [0], given: 15

If x≠0, is x^2/abs(x)<1? [#permalink]

08 Jan 2013, 04:12

If x ≠ 0, is x^2/abs(x)<1?
(1) x < 1
(2) x > −1

Question is came from GWD. My approach is time comsuming. So suggest me a quicker approch. Thanks

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11594

Followers: 1799

Kudos [?]: 9583 [0], given: 826

Re: If x≠0, is x^2/abs(x)<1? [#permalink]

08 Jan 2013, 04:30

curtis0063 wrote:

If x ≠ 0, is x^2/abs(x)<1?
(1) x < 1
(2) x > −1

Question is came from GWD. My approach is time comsuming. So suggest me a quicker approch. Thanks

Merging similar topics. Please refer to the solutions above.
_________________

Re: If x≠0, is x^2/abs(x)<1? [#permalink] 08 Jan 2013, 04:30

		Similar topics	Author	Replies	Last post
Similar Topics:		Is x negative? 1) x^3(1-x^2)<0 2) x^2-1<0	yezz	3	10 Oct 2006, 13:31
		Is x negative? (1) x^3(1-x^2) < 0 (2) x^2 - 1 < 0	above720	10	23 Aug 2007, 19:12
	1	Is x negative? 1. x^3(1-x^2)<0 2. x^2-1<0	vksunder	9	17 Jun 2008, 19:05
		Is x negative? 1) x^3(1-x^2)<0 2) x^2-1<0	yezz	1	16 Aug 2009, 00:45
	1	Is x negative? 1. X^3(1-x^2) < 0 2. x^2 - 1 < 0	etofu	5	27 Aug 2009, 19:35

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

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

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

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

Main navigation

GMAT Resources

Partners

MBA Resources