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:

a. 1 only b. 2 only. C. 3 only. D. 1 and 3 only. E.none

Responding to a pm:

Neither method needs to be used here. Just think of the definition of mod we use to remove the mod sign.

|x| = x if x >= 0 and |x| = -x if x < 0

We don't know whether a and b are positive or negative. |a|=|b| when absolute values of both a and b are the same. The signs can be different or same. There are 4 cases: a and b are positive, a is positive b is negative, a is negative b is positive, a and b are negative. For a must be true question, the relation should hold in every case.

1. a=b Doesn't hold when a and b have opposite signs. e.g. a = 5, b= -5

2.|a|=-b Doesn't hold when b is positive because -b will become negative while left hand side is always non negative. e.g. a = 5, b = 5 \(|5| \neq -5\)

3.-a=-b Doesn't hold when a and b have opposite signs. e.g. a = 5, b = -5 \(-5 \neq 5\)

a. 1 only b. 2 only. C. 3 only. D. 1 and 3 only. E.none

Responding to a pm:

Neither method needs to be used here. Just think of the definition of mod we use to remove the mod sign.

|x| = x if x >= 0 and |x| = -x if x < 0

We don't know whether a and b are positive or negative. |a|=|b| when absolute values of both a and b are the same. The signs can be different or same. There are 4 cases: a and b are positive, a is positive b is negative, a is negative b is positive, a and b are negative. For a must be true question, the relation should hold in every case.

1. a=b Doesn't hold when a and b have opposite signs. e.g. a = 5, b= -5

2.|a|=-b Doesn't hold when b is positive because -b will become negative while left hand side is always non negative. e.g. a = 5, b = 5 \(|5| \neq -5\)

3.-a=-b Doesn't hold when a and b have opposite signs. e.g. a = 5, b = -5 \(-5 \neq 5\)

Answer (E)

^^ by the highlighted statement above you mean that all the four cases you listed out should hold true for every stmt. 1. 2. 3. individually.

If yes then the only possible solution the to the question would be |a|=|b| , pl. re confirm ... thanks

^^ by the highlighted statement above you mean that all the four cases you listed out should hold true for every stmt. 1. 2. 3. individually.

If yes then the only possible solution the to the question would be |a|=|b| , pl. re confirm ... thanks

What I mean is that if we say any statement 'must be true' then it must hold for all 4 cases i.e. both a and b are positive, a is positive b is negative, a is negative b is positive and a and b are negative.

i.e. if statement 1 i.e. a = b must be true, then it should be true in all 4 cases.
_________________

^^ by the highlighted statement above you mean that all the four cases you listed out should hold true for every stmt. 1. 2. 3. individually.

If yes then the only possible solution the to the question would be |a|=|b| , pl. re confirm ... thanks

What I mean is that if we say any statement 'must be true' then it must hold for all 4 cases i.e. both a and b are positive, a is positive b is negative, a is negative b is positive and a and b are negative.

i.e. if statement 1 i.e. a = b must be true, then it should be true in all 4 cases.

Ok. thanks very much for the clarification... your blogs and posts are very informative

Thanks for the explanation. Had a query on this one. Suppose if numbers weren't chosen to evaluate this.

Consider: |a|= |b| this can be evaluated as: a,b have same signs or a,b have opposite signs

thus, a =b (same signs) and (a = -b or -a = b) for opposite signs.

|a| = -b would have two cases: a +ve , a -ve thus, a = -b or -a = -b => a = b. Thus, a = -b or -a=b AND a = b. which is what |a| = |b| boils down to.

Please help me understand if I'm missing anything.

\(|a|= |b|\) basically means that the distance between \(a\) and zero on the number line is the same as the distance between \(b\) and zero on the number line.

Thus either \(a=b\) (notice that it's the same as \(-a=-b\)) or \(a=-b\) (notice that it's the same as \(-a=b\)).

A. I only B. II only. C. III only. D. I and III only. E. None

Replace mod with its equivalent

We have one of these 4 equivalents for |a|=|b|:

-(a) = -(b) -(a) = b a = -(b) a=b

In the answer choices we can see that,

(i) is not the only possibility because we see there are other possibilities as seen above (ii) is equivalent to -(a) = -b or a = -b. Again these are not the only possibilities as we see there are other possibilities as seen above (iii) again is not the only possibility as there are other possibilities as seen above

Re: |a|=|b|, which of the following must be true : [#permalink]

Show Tags

16 Sep 2014, 20:44

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.
_________________

Re: |a|=|b|, which of the following must be true : [#permalink]

Show Tags

21 Sep 2015, 01:38

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.
_________________

Re: |a|=|b|, which of the following must be true : [#permalink]

Show Tags

30 Mar 2017, 10:40

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.
_________________