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:

If y + | y | = 0, which of the following must be true? [#permalink]

Show Tags

21 Apr 2012, 22:23

3

This post received KUDOS

Expert's post

boomtangboy wrote:

If y + | y | = 0, which of the following must be true? (A) y > 0 (B) y≥0 (C) y < 0 (D) y≤0 (E) y = 0

Why is just E incorrect?

Absolute value properties: When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

So, \(y+|y|=0\) --> \(|y|=-y\), which means that \(y\leq{0}\).

Answer: D.

As for your doubt: question asks which of the following MUST be true, not COULD be true. Since all negative values of y satisfy \(|y|=-y\) then it's not necessarily true that \(y=0\).

Re: If y + | y | = 0, which of the following must be true? [#permalink]

Show Tags

08 May 2012, 10:03

Bunuel wrote:

boomtangboy wrote:

If y + | y | = 0, which of the following must be true? (A) y > 0 (B) y≥0 (C) y < 0 (D) y≤0 (E) y = 0

Why is just E incorrect?

Absolute value properties: When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|\leq{-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|\leq{some \ expression}\). For example: \(|5|=5\);

So, \(y+|y|=0\) --> \(|y|=-y\), which means that \(y\leq{0}\).

Answer: D.

As for your doubt: question asks which of the following MUST be true, not COULD be true. Since all negative values of y satisfy \(|y|=-y\) then it's not necessarily true that \(y=0\).

Hope it's clear.

Hi ,

Thanks for the clear and concise explaination.

Just wanted to clarify one thing.

In mods the two conditions I know are applied include; If x<0 or if x>=0. However in the above explaination you have used x<=0. Was that used for some particular reason or my concepts of absolute values are incorrect.

Re: If y + | y | = 0, which of the following must be true? [#permalink]

Show Tags

09 May 2012, 08:10

Bunuel wrote:

boomtangboy wrote:

If y + | y | = 0, which of the following must be true? (A) y > 0 (B) y≥0 (C) y < 0 (D) y≤0 (E) y = 0

Why is just E incorrect?

Absolute value properties: When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|\leq{-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|\leq{some \ expression}\). For example: \(|5|=5\);

So, \(y+|y|=0\) --> \(|y|=-y\), which means that \(y\leq{0}\).

Answer: D.

As for your doubt: question asks which of the following MUST be true, not COULD be true. Since all negative values of y satisfy \(|y|=-y\) then it's not necessarily true that \(y=0\).

Hope it's clear.

Hi Bunuel, why are we considering the case of y=0, as if y=0, then the expression |y|=-y makes no sense, because |0|=0. and there is no +0 or -0. Please explain. Thanks in advance.

Re: If y + | y | = 0, which of the following must be true? [#permalink]

Show Tags

09 May 2012, 08:26

Expert's post

piyushksharma wrote:

Bunuel wrote:

boomtangboy wrote:

If y + | y | = 0, which of the following must be true? (A) y > 0 (B) y≥0 (C) y < 0 (D) y≤0 (E) y = 0

Why is just E incorrect?

Absolute value properties: When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|\leq{-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|\leq{some \ expression}\). For example: \(|5|=5\);

So, \(y+|y|=0\) --> \(|y|=-y\), which means that \(y\leq{0}\).

Answer: D.

As for your doubt: question asks which of the following MUST be true, not COULD be true. Since all negative values of y satisfy \(|y|=-y\) then it's not necessarily true that \(y=0\).

Hope it's clear.

Hi Bunuel, why are we considering the case of y=0, as if y=0, then the expression |y|=-y makes no sense, because |0|=0. and there is no +0 or -0. Please explain. Thanks in advance.

Not, so. You can write |0|=-0 and there is nothing wrong in that. _________________

Re: If y + | y | = 0, which of the following must be true? [#permalink]

Show Tags

09 May 2012, 08:33

Bunuel wrote:

Not, so. You can write |0|=-0 and there is nothing wrong in that.

hm, absolute value of an integer means how far this integer is from zero. so, absolute value of zero iz zero, since zero is zero far from zero (sounds like a quote of Alice from Wonderland hehe) -0 looks weird to me, since zero is neither positive, nor negative, and has no sigh. But still, I wont claim that my way of thinking is right. I will believe to Bunuel )) amazing life, every day is a new discovery ) _________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Re: If y + | y | = 0, which of the following must be true? [#permalink]

Show Tags

15 May 2012, 04:32

I have a question here.. if the the question was y + |y| = 2y , then can we say y>=0? given then 0+0 = 2(0). Please let me know in case I am doing something wrong. Thanks in advance.

Re: If y + | y | = 0, which of the following must be true? [#permalink]

Show Tags

15 May 2012, 04:45

Expert's post

pavanpuneet wrote:

I have a question here.. if the the question was y + |y| = 2y , then can we say y>=0? given then 0+0 = 2(0). Please let me know in case I am doing something wrong. Thanks in advance.

Re: If y + | y | = 0, which of the following must be true? [#permalink]

Show Tags

21 Apr 2016, 05:45

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. _________________

So, my final tally is in. I applied to three b schools in total this season: INSEAD – admitted MIT Sloan – admitted Wharton – waitlisted and dinged No...

A few weeks ago, the following tweet popped up in my timeline. thanks @Uber_Mumbai for showing me what #daylightrobbery means!I know I have a choice not to use it...

“This elective will be most relevant to learn innovative methodologies in digital marketing in a place which is the origin for major marketing companies.” This was the crux...