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 500,000 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:

Re: Inequality...involving reciprocals [#permalink]
15 Jan 2012, 05:35

3

This post received KUDOS

Expert's post

Apoorva81 wrote:

Is 1/x-y < y - x ?

(1) y is positive. (2) x is negative.

can you please provide detailed explanation..??

Is \(\frac{1}{x-y}<y - x\)?

(1) \(y\) is positive, clearly insufficient, as no info about \(x\); (2) \(x\) is negative, also insufficient, as no info about \(y\);

(1)+(2) We have \(y=positive\) and \(x=negative\), thus \(y>x\) (this can be rewritten as \(y-x>0\) or \(0>x-y\)). Now: \(LHS=\frac{1}{x-y}=\frac{1}{negative}=negative\), and \(RHS=y-x=positive\) thus \(\frac{1}{x-y}=negative<y-x=positive\). Sufficient.

In order to separate your x's and y's from each other, you need to know which term is larger. This is because you need to know whether x-y or y-x is negative (one of them will be, unless they are equal). Taking both statements together, you know that the two variables are not equal, and you can manipulate the inequality, keeping in mind that you need to flip the sign when multiplying or dividing by a negative number. _________________

I explained it in kind of a backwards way. The first thing you need to know in that problem is whether x and y are equal. No single statement tells you that.

Sorry for the double post, but it seems I can't edit my previous post while viewing the forum with Tapatalk.

Sent from my HTC Glacier using Tapatalk 2 _________________

Re: Inequality...involving reciprocals [#permalink]
09 May 2014, 07:38

Bunuel wrote:

Apoorva81 wrote:

Is 1/x-y < y - x ?

(1) y is positive. (2) x is negative.

can you please provide detailed explanation..??

Is \(\frac{1}{x-y}<y - x\)?

(1) \(y\) is positive, clearly insufficient, as no info about \(x\); (2) \(x\) is negative, also insufficient, as no info about \(y\);

(1)+(2) We have \(y=positive\) and \(x=negative\), thus \(y>x\) (this can be rewritten as \(y-x>0\) or \(0>x-y\)). Now: \(LHS=\frac{1}{x-y}=\frac{1}{negative}=negative\), and \(RHS=y-x=positive\) thus \(\frac{1}{x-y}=negative<y-x=positive\). Sufficient.

Answer: C.

Why can't we do the following rephrase?

1/(x-y) < (y-x)

-1/(y-x) < (y-x)

-1 < (y-x)^2

since the RHS is a square, irrespective of x and y values the equation is satisfied.

Re: Inequality...involving reciprocals [#permalink]
09 May 2014, 08:25

1

This post received KUDOS

Expert's post

rishiroadster wrote:

Bunuel wrote:

Apoorva81 wrote:

Is 1/x-y < y - x ?

(1) y is positive. (2) x is negative.

can you please provide detailed explanation..??

Is \(\frac{1}{x-y}<y - x\)?

(1) \(y\) is positive, clearly insufficient, as no info about \(x\); (2) \(x\) is negative, also insufficient, as no info about \(y\);

(1)+(2) We have \(y=positive\) and \(x=negative\), thus \(y>x\) (this can be rewritten as \(y-x>0\) or \(0>x-y\)). Now: \(LHS=\frac{1}{x-y}=\frac{1}{negative}=negative\), and \(RHS=y-x=positive\) thus \(\frac{1}{x-y}=negative<y-x=positive\). Sufficient.

Answer: C.

Why can't we do the following rephrase?

1/(x-y) < (y-x)

-1/(y-x) < (y-x)

-1 < (y-x)^2

since the RHS is a square, irrespective of x and y values the equation is satisfied.

The point is that we don't know whether y-x is positive or negative. If it's positive, then yes we'd have -1 < (y-x)^2 but if it's negative, then we'd have -1 > (y-x)^2 (flip the sign when multiplying by negative value).

Never multiply (or reduce) an inequality by variable (or by an expression with variable) if you don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero. _________________

Re: Is 1/(x-y) < (y-x) ? [#permalink]
09 Aug 2014, 02:31

alphonsa wrote:

With the way you put it, this question seemed like a below 500 question :\

I don't know why I took so long to decipher it was option C .

It happens to the best of people especially if the question is done during exam time.... One more thing..I think you need to look at these links for books for your preparation

Re: Is 1/(x-y) < (y - x) ? [#permalink]
25 Aug 2015, 21:48

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. _________________

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

http://blog.davidbbaker.com/wp-content/uploads/2015/11/12249800_10153820891439090_8007573611012789132_n.jpg When you think about an MBA program, usually the last thing you think of is professional collegiate sport. (Yes American’s I’m going...

Every student has a predefined notion about a MBA degree:- hefty packages, good job opportunities, improvement in position and salaries but how many really know the journey of becoming...