Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If x<>0, is |x| <1? (1) x^2<1 (2) |x| < 1/x From (1) x^2 <1, x is either a positive fraction or a negaive fraction. In both cases, the modulus will be less than 1. So Statement 1 is sufficient.

From (2), |x| < 1/x, two cases: Case 1: x < 1/x x^2 < 1 x^2 - 1<0 (x+1)(x-1) <0 -1<x<1 <-- so always less than 1

Case 2: -x < 1/x -x^2 < 1 x^2 > 1 x^2 - 1 > 0 (x+1)(x-1) > 0 x < -1 or x > 1 <-- not always less than 1. More than 2 solutions using statement 2, so not sufficient. Ans: A

If x<>0, is |x| <1?

ok, here from i, it is clear that x^2 is positive and fraction is the only positive less than 1 and sqrt of any positive fraction is also positive fraction. so i is sufficient to say that x<1 and so does lxl.

from ii, if |x| < 1/x, then x cannot be -ve. because if x is negative, then 1/x cannot be >lxl because lxl is always positive. so sufficient.....

If x<>0, is |x| <1? (1) x^2<1 (2) |x| < 1/x From (1) x^2 <1, x is either a positive fraction or a negaive fraction. In both cases, the modulus will be less than 1. So Statement 1 is sufficient.

From (2), |x| < 1/x, two cases: Case 1: x < 1/x x^2 < 1 x^2 - 1<0 (x+1)(x-1) <0 -1<x<1 <-- so always less than 1

Case 2: -x < 1/x -x^2 < 1 x^2 > 1 x^2 - 1 > 0 (x+1)(x-1) > 0 x < -1 or x > 1 <-- not always less than 1. More than 2 solutions using statement 2, so not sufficient. Ans: A

If x<>0, is |x| <1?

ok, here from i, it is clear that x^2 is positive and fraction is the only positive less than 1 and sqrt of any positive fraction is also positive fraction. so i is sufficient to say that x<1 and so does lxl.

from ii, if |x| < 1/x, then x cannot be -ve. because if x is negative, then 1/x cannot be >lxl because lxl is always positive. so sufficient.....

Ha!! Yes, I miss the negative part out. Sorry!! I've been out of touch with GMAT maths for quite a while!

Re: DS - Absolute Value [#permalink]
16 Oct 2005, 08:37

rahulraao wrote:

What is the value of |x|?

(1) x = -|x| (2) x^2 = 4

B

A) Insuff. x can be any negative number. B) x=2 or -2. Since |2| or |-2| are both = 2, B is suff.

rahulraao wrote:

If x<>0, is |x| <1?

(1) x^2<1 (2) |x| < 1/x

D

A) Suff. since x^2<1, x should be -1 < x < 1. |x| is always less than 1
B) Suff. x has to be a fraction.
If x= -1/2
1/2 < -2 which is false. So x must be positive
If x=1/2
1/2 < 2 true.
If x = 3 or -3
3 < 1/3 or -1/3 Not true.
From above, we know x is a positive fraction (<1) So |x| <1

Wow...I'm still reeling from my HBS admit . Thank you once again to everyone who has helped me through this process. Every year, USNews releases their rankings of...

Almost half of MBA is finally coming to an end. I still have the intensive Capstone remaining which started this week, but things have been ok so far...