GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Sep 2018, 06:46

### 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

# M15-37

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49204

### Show Tags

16 Sep 2014, 00:57
1
10
00:00

Difficulty:

95% (hard)

Question Stats:

43% (01:10) correct 57% (01:06) wrong based on 136 sessions

### HideShow timer Statistics

$$a^2 - b^2 = b^2 - c^2$$. Is $$a = |b|$$?

(1) $$b = |c|$$

(2) $$b = |a|$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49204

### Show Tags

16 Sep 2014, 00:58
2
1
Official Solution:

Statement (1) by itself is insufficient. From S1 we know that $$a^2 - b^2 = 0$$. From here we can only conclude that $$|a| = |b|$$.

Statement (2) by itself is insufficient. From S2 we know that $$b$$ is non-negative. But whether $$a$$ is non-negative remains a question.

Statements (1) and (2) combined are insufficient. Consider $$a = b = c = 1$$ (the answer to the question is "yes") and $$a = -1$$, $$b = c = 1$$ (the answer to the question is "no").

_________________
Intern
Joined: 03 Mar 2013
Posts: 9

### Show Tags

16 Sep 2014, 07:40
Hi

Can the original st a = |b| translated to a=sqrt(b^2) or a^2= b^2 ?
In which case St A will suffice:
b = |c|
b^2=c^2

a^2 - b^2 = b^2 - c^2
or, a^2 - c^2 = b^2 - c^2
or, a^2=b^2
Sufficient
Math Expert
Joined: 02 Sep 2009
Posts: 49204

### Show Tags

16 Sep 2014, 13:49
sidinsin wrote:
Hi

Can the original st a = |b| translated to a=sqrt(b^2) or a^2= b^2 ?
In which case St A will suffice:
b = |c|
b^2=c^2

a^2 - b^2 = b^2 - c^2
or, a^2 - c^2 = b^2 - c^2
or, a^2=b^2
Sufficient

No. It's possible a^2 to be equal to b^2 and a not be equal to |b|. For example, a=-1 and b=1.
_________________
Retired Moderator
Joined: 18 Sep 2014
Posts: 1152
Location: India

### Show Tags

04 Jul 2015, 10:33
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. From S1 we know that $$a^2 - b^2 = 0$$. From here we can only conclude that $$|a| = |b|$$.

Statement (2) by itself is insufficient. From S2 we know that $$b$$ is non-negative. But whether $$a$$ is non-negative remains a question.

Statements (1) and (2) combined are insufficient. Consider $$a = b = c = 1$$ (the answer to the question is "yes") and $$a = -1$$, $$b = c = 1$$ (the answer to the question is "no").

My doubt may sound silly but this is confusing me a lot.
what is the difference between

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

_________________

The only time you can lose is when you give up. Try hard and you will suceed.
Thanks = Kudos. Kudos are appreciated

http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html
When you post a question Pls. Provide its source & TAG your questions
Avoid posting from unreliable sources.

My posts
http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924
http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html
http://gmatclub.com/forum/possessive-pronouns-200496.html
http://gmatclub.com/forum/double-negatives-206717.html
http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773

Math Expert
Joined: 02 Sep 2009
Posts: 49204

### Show Tags

05 Jul 2015, 08:39
1
1
Mechmeera wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. From S1 we know that $$a^2 - b^2 = 0$$. From here we can only conclude that $$|a| = |b|$$.

Statement (2) by itself is insufficient. From S2 we know that $$b$$ is non-negative. But whether $$a$$ is non-negative remains a question.

Statements (1) and (2) combined are insufficient. Consider $$a = b = c = 1$$ (the answer to the question is "yes") and $$a = -1$$, $$b = c = 1$$ (the answer to the question is "no").

My doubt may sound silly but this is confusing me a lot.
what is the difference between

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

1. $$|a| = |b|$$ means that the distance from a to 0 is the same as the distance from b to 0. Or that the magnitudes of a and b are the same.

2. $$a = |b|$$ means that the distance from b to 0 is a.

3. $$|a| = b$$ means that the distance from a to 0 is b.
_________________
Intern
Joined: 05 Jan 2015
Posts: 12
Location: India
WE: Engineering (Energy and Utilities)

### Show Tags

23 Nov 2015, 21:55
Hi

Can the solution be bit more elaborative ,Step by step. I'm finding it difficult to understand.
Intern
Joined: 23 Mar 2015
Posts: 9

### Show Tags

23 Jun 2016, 01:43
Hi,
The question asked is "Is a = mod b"
This can be written as is a=+b or a=-b

1) From 1, b = mod c

so, b = +c or b=-c

hence, b2=c2
hence the given equation, "a2-b2=b2-c2" or (a2+c2)/2=b2
becomes a2=b2
this would mean that a=b or a=-b

Similarly using 2nd also we can prove.

Why is my way wrong?
Math Expert
Joined: 02 Sep 2009
Posts: 49204

### Show Tags

23 Jun 2016, 01:55
gauravprashar17 wrote:
Hi,
The question asked is "Is a = mod b"
This can be written as is a=+b or a=-b

1) From 1, b = mod c

so, b = +c or b=-c

hence, b2=c2
hence the given equation, "a2-b2=b2-c2" or (a2+c2)/2=b2
becomes a2=b2
this would mean that a=b or a=-b

Similarly using 2nd also we can prove.

Why is my way wrong?

Check here: m15-184069.html#p1416891
_________________
Senior Manager
Joined: 31 Mar 2016
Posts: 396
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

### Show Tags

22 Aug 2016, 04:40
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 16 Feb 2012
Posts: 22
GMAT 1: 650 Q47 V33

### Show Tags

18 Dec 2016, 11:59
Bunuel,
I would like to add one more point to the wonderful explanation provided by you.
Using S1, we can actually deduce |A| = |B| = |C|.
Thanks !
Manager
Joined: 18 Dec 2016
Posts: 102
GMAT 1: 760 Q50 V41
GPA: 3.3

### Show Tags

19 Mar 2017, 22:09
Is there a link explaining the mod theory and related problems? I have been getting most of the questions wrong in this section.
Math Expert
Joined: 02 Sep 2009
Posts: 49204

### Show Tags

20 Mar 2017, 00:50
1
1
gmat2k17 wrote:
Is there a link explaining the mod theory and related problems? I have been getting most of the questions wrong in this section.

Hope it helps.
_________________
Manager
Joined: 18 Dec 2016
Posts: 102
GMAT 1: 760 Q50 V41
GPA: 3.3

### Show Tags

20 Mar 2017, 06:39
Bunuel wrote:
gmat2k17 wrote:
Is there a link explaining the mod theory and related problems? I have been getting most of the questions wrong in this section.

Hope it helps.

Perfect, thanks Bunuel
Intern
Joined: 09 Sep 2015
Posts: 24

### Show Tags

21 Mar 2017, 06:41
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. From S1 we know that $$a^2 - b^2 = 0$$. From here we can only conclude that $$|a| = |b|$$.

Statement (2) by itself is insufficient. From S2 we know that $$b$$ is non-negative. But whether $$a$$ is non-negative remains a question.

Statements (1) and (2) combined are insufficient. Consider $$a = b = c = 1$$ (the answer to the question is "yes") and $$a = -1$$, $$b = c = 1$$ (the answer to the question is "no").

Hi Bunuel,

In Statement 1, how are we arriving at a^2-b^2=0 ? And would you please elaborate explanation for statement 2 as well.

Thanks
Amaresh
Math Expert
Joined: 02 Sep 2009
Posts: 49204

### Show Tags

21 Mar 2017, 06:51
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. From S1 we know that $$a^2 - b^2 = 0$$. From here we can only conclude that $$|a| = |b|$$.

Statement (2) by itself is insufficient. From S2 we know that $$b$$ is non-negative. But whether $$a$$ is non-negative remains a question.

Statements (1) and (2) combined are insufficient. Consider $$a = b = c = 1$$ (the answer to the question is "yes") and $$a = -1$$, $$b = c = 1$$ (the answer to the question is "no").

Hi Bunuel,

In Statement 1, how are we arriving at a^2-b^2=0 ? And would you please elaborate explanation for statement 2 as well.

Thanks
Amaresh

From the stem we know that $$a^2 - b^2 = b^2 - c^2$$. From (1) $$b = |c|$$ means that $$b^2=c^2$$. Substitute: $$a^2 - b^2 = b^2 - b^2=0$$

As for (2): $$b = |a|$$. Given that b is equal to an absolute value of a number. An absolute value cannot be negative, theretofore $$b$$ is non-negative.

Hope it's clear.
_________________
Manager
Joined: 17 May 2017
Posts: 136
GPA: 3

### Show Tags

26 Jul 2017, 13:17
This is really the toughest DS question i solved
thank you Bunuel for this question
Intern
Joined: 31 Mar 2018
Posts: 3
Location: India
Concentration: Sustainability, General Management
Schools: Erasmus '20
GMAT 1: 550 Q44 V23
GMAT 2: 660 Q44 V38
GMAT 3: 710 Q47 V41
GPA: 3
WE: Architecture (Other)

### Show Tags

15 Apr 2018, 04:49
$$a^2$$ -$$b^2$$ =$$b^2-c^2$$

so, $$(a-b)(a+b)=(b-c)(b+c)$$

its given that (1) $$b=|c|$$

so, $$(a-b)(a+b) = 0$$
i.e, $$a=b$$ or $$a = -b$$, or $$a= |b|$$,

So , isn't (1) sufficient ?
Manager
Joined: 26 Feb 2018
Posts: 53
Location: India
GMAT 1: 560 Q41 V27
WE: Web Development (Computer Software)

### Show Tags

17 Jun 2018, 12:32
I think this is a high-quality question and I agree with explanation.
Re M15-37 &nbs [#permalink] 17 Jun 2018, 12:32
Display posts from previous: Sort by

# M15-37

Moderators: chetan2u, Bunuel

# Events & Promotions

 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®.