Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47077

Question Stats:
43% (01:10) correct 57% (01:06) wrong based on 136 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 47077

Re M1537 [#permalink]
Show Tags
16 Sep 2014, 00:58



Intern
Joined: 03 Mar 2013
Posts: 9

Re: M1537 [#permalink]
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: 47077

Re: M1537 [#permalink]
Show Tags
16 Sep 2014, 13:49



Retired Moderator
Joined: 18 Sep 2014
Posts: 1165
Location: India

Re: M1537 [#permalink]
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 nonnegative. But whether \(a\) is nonnegative 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").
Answer: E My doubt may sound silly but this is confusing me a lot. what is the difference between 1. \(a = b\). 2. \(a = b\). 3. \(a = b\). please explain the concept.
_________________
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/rulesforpostinginverbalgmatforum134642.html When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources.
My posts http://gmatclub.com/forum/beautyofcoordinategeometry213760.html#p1649924 http://gmatclub.com/forum/callingallmarchaprilgmattakerswhowanttocross213154.html http://gmatclub.com/forum/possessivepronouns200496.html http://gmatclub.com/forum/doublenegatives206717.html http://gmatclub.com/forum/thegreatestintegerfunction223595.html#p1721773 https://gmatclub.com/forum/improvereadinghabit233410.html#p1802265



Math Expert
Joined: 02 Sep 2009
Posts: 47077

Re: M1537 [#permalink]
Show Tags
05 Jul 2015, 08:39
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 nonnegative. But whether \(a\) is nonnegative 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").
Answer: E My doubt may sound silly but this is confusing me a lot. what is the difference between 1. \(a = b\). 2. \(a = b\). 3. \(a = b\). please explain the concept. 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 05 Jan 2015
Posts: 12
Location: India
Concentration: International Business, Marketing
WE: Engineering (Energy and Utilities)

Re: M1537 [#permalink]
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

Re: M1537 [#permalink]
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, "a2b2=b2c2" 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: 47077

Re: M1537 [#permalink]
Show Tags
23 Jun 2016, 01:55



Senior Manager
Joined: 31 Mar 2016
Posts: 400
Location: India
Concentration: Operations, Finance
GPA: 3.8
WE: Operations (Commercial Banking)

Re M1537 [#permalink]
Show Tags
22 Aug 2016, 04:40
I think this is a highquality question and I agree with explanation.



Intern
Joined: 16 Feb 2012
Posts: 14

Re: M1537 [#permalink]
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. Please correct me if wrong. Thanks !



Manager
Joined: 18 Dec 2016
Posts: 102
GPA: 3.3

Re: M1537 [#permalink]
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: 47077

Re: M1537 [#permalink]
Show Tags
20 Mar 2017, 00:50



Manager
Joined: 18 Dec 2016
Posts: 102
GPA: 3.3

Re: M1537 [#permalink]
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: 25

Re: M1537 [#permalink]
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 nonnegative. But whether \(a\) is nonnegative 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").
Answer: E Hi Bunuel, In Statement 1, how are we arriving at a^2b^2=0 ? And would you please elaborate explanation for statement 2 as well. Thanks Amaresh



Math Expert
Joined: 02 Sep 2009
Posts: 47077

Re: M1537 [#permalink]
Show Tags
21 Mar 2017, 06:51
amargad0391 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 nonnegative. But whether \(a\) is nonnegative 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").
Answer: E Hi Bunuel, In Statement 1, how are we arriving at a^2b^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 nonnegative. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 17 May 2017
Posts: 144
GPA: 3

Re: M1537 [#permalink]
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: General Management, Strategy
WE: Architecture (Other)

Re: M1537 [#permalink]
Show Tags
15 Apr 2018, 04:49
\(a^2\) \(b^2\) =\(b^2c^2\)
so, \((ab)(a+b)=(bc)(b+c)\)
its given that (1) \(b=c\)
so, \((ab)(a+b) = 0\) i.e, \(a=b\) or \(a = b\), or \(a= b\),
So , isn't (1) sufficient ?



Manager
Joined: 26 Feb 2018
Posts: 53
Location: India
WE: Web Development (Computer Software)

Re M1537 [#permalink]
Show Tags
17 Jun 2018, 12:32
I think this is a highquality question and I agree with explanation.










