It is currently 23 Oct 2017, 03:02

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# |a|=|b|, which of the following must be true :

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 29 Aug 2012
Posts: 26

Kudos [?]: 35 [3], given: 56

Schools: Babson '14
GMAT Date: 02-28-2013
|a|=|b|, which of the following must be true : [#permalink]

### Show Tags

28 Oct 2012, 12:06
3
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

58% (00:33) correct 42% (00:27) wrong based on 861 sessions

### HideShow timer Statistics

|a|=|b|, which of the following must be true :

I. a=b
II. |a|=-b
III. -a=-b

A. I only
B. II only.
C. III only.
D. I and III only.
E. None
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Oct 2012, 00:58, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 35 [3], given: 56

Intern
Joined: 28 Oct 2012
Posts: 15

Kudos [?]: 35 [0], given: 1

Re: Modulus Ques. [#permalink]

### Show Tags

28 Oct 2012, 12:27
E

Let's say l a l = 1 and l b l = 1

For l a l = 1 ; a can be 1 or -1
Similarly b can be 1 or -1

This reasoning is used to get the answer

Kudos [?]: 35 [0], given: 1

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7677

Kudos [?]: 17399 [15], given: 232

Location: Pune, India
Re: Modulus Ques. [#permalink]

### Show Tags

28 Oct 2012, 23:00
15
KUDOS
Expert's post
2
This post was
BOOKMARKED
himanshuhpr wrote:
|a|=|b| , which of the following must be true :

1. a=b 2.|a|=-b 3.-a=-b

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
$$-5 \neq 5$$

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17399 [15], given: 232 Intern Joined: 29 Aug 2012 Posts: 26 Kudos [?]: 35 [0], given: 56 Schools: Babson '14 GMAT Date: 02-28-2013 Re: Modulus Ques. [#permalink] ### Show Tags 29 Oct 2012, 00:21 1 This post was BOOKMARKED VeritasPrepKarishma wrote: himanshuhpr wrote: |a|=|b| , which of the following must be true : 1. a=b 2.|a|=-b 3.-a=-b 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 Kudos [?]: 35 [0], given: 56 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7677 Kudos [?]: 17399 [0], given: 232 Location: Pune, India Re: Modulus Ques. [#permalink] ### Show Tags 29 Oct 2012, 02:03 himanshuhpr wrote: ^^ 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 17399 [0], given: 232

Intern
Joined: 29 Aug 2012
Posts: 26

Kudos [?]: 35 [0], given: 56

Schools: Babson '14
GMAT Date: 02-28-2013
Re: Modulus Ques. [#permalink]

### Show Tags

29 Oct 2012, 02:08
VeritasPrepKarishma wrote:
himanshuhpr wrote:
^^ 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

Kudos [?]: 35 [0], given: 56

Intern
Joined: 15 Oct 2011
Posts: 41

Kudos [?]: 9 [0], given: 37

Re: Modulus Ques. [#permalink]

### Show Tags

29 Oct 2012, 10:49
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.

Kudos [?]: 9 [0], given: 37

Math Expert
Joined: 02 Sep 2009
Posts: 41910

Kudos [?]: 129406 [1], given: 12201

Re: Modulus Ques. [#permalink]

### Show Tags

29 Oct 2012, 11:03
1
KUDOS
Expert's post
prep wrote:
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.

$$|a|= |b|$$ 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 $$-a=b$$).

Hope it helps.
_________________

Kudos [?]: 129406 [1], given: 12201

Senior Manager
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 542 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: |a|=|b|, which of the following must be true : [#permalink]

### Show Tags

05 Dec 2012, 01:52
|a|=|b|

The equation doesn't tell us anything about the sign of a and b. All we know is that their absolute values are equal.

Possibilities:
|-5| = |5|
|5| = |5|
|5| = |-5|

I. a=b ==> When a=5 and b=-5, this is false!
II. |a|=-b ==> When a=-5 and b=5, this is false!
III. -a=-b ==> When a=-5 and b=5, this is false!

Answer: NONE or E
_________________

Impossible is nothing to God.

Kudos [?]: 542 [0], given: 11

Math Expert
Joined: 02 Sep 2009
Posts: 41910

Kudos [?]: 129406 [0], given: 12201

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

### Show Tags

04 Jul 2013, 01:45
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

_________________

Kudos [?]: 129406 [0], given: 12201

Director
Joined: 17 Dec 2012
Posts: 608

Kudos [?]: 518 [0], given: 16

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

### Show Tags

04 Jul 2013, 18:33
himanshuhpr wrote:
|a|=|b|, which of the following must be true :

I. a=b
II. |a|=-b
III. -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

So the answer is E.
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Pay After Use
Standardized Approaches

Kudos [?]: 518 [0], given: 16

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16543

Kudos [?]: 274 [0], given: 0

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.
_________________

Kudos [?]: 274 [0], given: 0

Intern
Joined: 22 Jul 2014
Posts: 22

Kudos [?]: 2 [0], given: 13

GMAT 1: 450 Q38 V12
WE: Information Technology (Computer Software)
Re: |a|=|b|, which of the following must be true : [#permalink]

### Show Tags

20 Sep 2014, 22:57
Where am i going wrong ??

|a| = |b|
$$\sqrt{a^2}$$ = $$\sqrt{b^2}$$
$$a^2$$ = $$b^2$$
a=b
_________________

Failures are stepping stones to success !!!

Kudos [?]: 2 [0], given: 13

Math Expert
Joined: 02 Sep 2009
Posts: 41910

Kudos [?]: 129406 [0], given: 12201

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

### Show Tags

21 Sep 2014, 00:09
prashd wrote:
Where am i going wrong ??

|a| = |b|
$$\sqrt{a^2}$$ = $$\sqrt{b^2}$$
$$a^2$$ = $$b^2$$
a=b

Have you checked this: a-b-which-of-the-following-must-be-true-141468.html#p1137162

a^2 = b^2 does not necessarily means that a = b. Consider a = 1 and b = -1. a^2 = b^2 means a = b or a = -b.
_________________

Kudos [?]: 129406 [0], given: 12201

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16543

Kudos [?]: 274 [0], given: 0

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.
_________________

Kudos [?]: 274 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16543

Kudos [?]: 274 [0], given: 0

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.
_________________

Kudos [?]: 274 [0], given: 0

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1655

Kudos [?]: 852 [1], given: 3

Location: United States (CA)
Re: |a|=|b|, which of the following must be true : [#permalink]

### Show Tags

04 Apr 2017, 16:18
1
KUDOS
Expert's post
himanshuhpr wrote:
|a|=|b|, which of the following must be true :

I. a=b
II. |a|=-b
III. -a=-b

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

Since |a| = |b|, we see that a = b, -a = b, a = -b, or -a = -b.

Since we have all four of those options as possibilities, none of the Roman numerals MUST BE TRUE.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 852 [1], given: 3

Re: |a|=|b|, which of the following must be true :   [#permalink] 04 Apr 2017, 16:18
Display posts from previous: Sort by

# |a|=|b|, which of the following must be true :

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.