December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL. December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51121

Question Stats:
21% (01:16) correct 79% (01:53) wrong based on 192 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Official Solution:If \(6a=3b=7c\), what is the value of \(a+b+c\)?Given: \(6a=3b=7c\). The least common multiple of 6, 3, and 7 is 42, hence we can write: \(6a=3b=7c=42x\), for some number \(x\). So, \(a=7x\), \(b=14x\) and \(c=6x\). (1) \(ac=6b\) \(7x*6x=6*14x\); \(x^2=2x\); \(x=0\) or \(x=2\). Not sufficient. (2) \(5b=8a+4c\) \(5*14x=8*7x+4*6x\); \(70x=80x\); \(10x=0\); \(x=0\), hence \(a=b=c=0\) and \(a+b+c=0\). Sufficient. Answer: 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



Current Student
Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65

Re: M2721
[#permalink]
Show Tags
13 Nov 2014, 19:50
Hey Bunuel,
Can u explain why this question turned out to ratio problem, as described.
On first inference it seems like a variable Question with three variables in an equated expression "6a = 3b =7c". And statement A says "ac = 6b" which solves to c = 12 (ac = 6 x 2a => c = 12 & b = 28 & a = 14) and a+b+c = 54.
statement 2 does not make sense in this scenario.
so answer to this comes as "A".
can you explain how to infer this question so that it dosent go either way.



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Alaukik wrote: Hey Bunuel,
Can u explain why this question turned out to ratio problem, as described.
On first inference it seems like a variable Question with three variables in an equated expression "6a = 3b =7c". And statement A says "ac = 6b" which solves to c = 12 (ac = 6 x 2a => c = 12 & b = 28 & a = 14) and a+b+c = 54.
statement 2 does not make sense in this scenario.
so answer to this comes as "A".
can you explain how to infer this question so that it dosent go either way. You cannot reduce ac = 12a by a and write c = 12 as you exclude possibility of a=0 > a(c12)=0 > either a=0 OR c=12. So, we get either a=b=c=0 or a=14, b=28 and c=12. So, the first statement is not sufficient. 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



Current Student
Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65

Re: M2721
[#permalink]
Show Tags
14 Nov 2014, 02:27
Bunuel wrote: Alaukik wrote: Hey Bunuel,
Can u explain why this question turned out to ratio problem, as described.
On first inference it seems like a variable Question with three variables in an equated expression "6a = 3b =7c". And statement A says "ac = 6b" which solves to c = 12 (ac = 6 x 2a => c = 12 & b = 28 & a = 14) and a+b+c = 54.
statement 2 does not make sense in this scenario.
so answer to this comes as "A".
can you explain how to infer this question so that it dosent go either way. You can not reduce ac = 12a by a and write c = 12 as you exclude possibility of a=0 > a(c12)=0 > either a=0 OR c=12. So, we get either a=b=c=0 or a=14, b=28 and c=12. So, the first statement is not sufficient. Hope it's clear. Oh yes. I discounted the other possibility.. This leaves BCE as answer. can you help me understand if we can use the Statement 2 to arrive at the answer in the method i was following? So in statement 2, on sperating and adding the original equation "6a=3b=7c" , we can get "6a+3b=14c" and using equation from satement 2 we can solve both as 6a = 58c => that only possibility is zero? as "6a = 7c" already? or we go to "C" both together and substitute value c = 0 & 12 to prove that only zero makes sense and with numerical values LHS != RHS? just asking mathematically. I know answer has to come B only.



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: M2721
[#permalink]
Show Tags
14 Nov 2014, 04:43
Alaukik wrote: Bunuel wrote: Alaukik wrote: Hey Bunuel,
Can u explain why this question turned out to ratio problem, as described.
On first inference it seems like a variable Question with three variables in an equated expression "6a = 3b =7c". And statement A says "ac = 6b" which solves to c = 12 (ac = 6 x 2a => c = 12 & b = 28 & a = 14) and a+b+c = 54.
statement 2 does not make sense in this scenario.
so answer to this comes as "A".
can you explain how to infer this question so that it dosent go either way. You can not reduce ac = 12a by a and write c = 12 as you exclude possibility of a=0 > a(c12)=0 > either a=0 OR c=12. So, we get either a=b=c=0 or a=14, b=28 and c=12. So, the first statement is not sufficient. Hope it's clear. Oh yes. I discounted the other possibility.. This leaves BCE as answer. can you help me understand if we can use the Statement 2 to arrive at the answer in the method i was following? So in statement 2, on sperating and adding the original equation "6a=3b=7c" , we can get "6a+3b=14c" and using equation from satement 2 we can solve both as 6a = 58c => that only possibility is zero? as "6a = 7c" already? or we go to "C" both together and substitute value c = 0 & 12 to prove that only zero makes sense and with numerical values LHS != RHS? just asking mathematically. I know answer has to come B only. Not quite following what you are trying to say but from (2) the only possible case is a=b=c=0.
_________________
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



Current Student
Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65

Re: M2721
[#permalink]
Show Tags
14 Nov 2014, 05:32
Well I was trying to say that the equation and condition in question stem were contradicting in Statement 2. so yes, only a=b=c=0 comes as solution for "B".
Thanks.



Intern
Joined: 07 Dec 2014
Posts: 9

Re: M2721
[#permalink]
Show Tags
07 May 2016, 07:36
Bunuel wrote: Official Solution:
If \(6a=3b=7c\), what is the value of \(a+b+c\)?
Given: \(6a=3b=7c\). The least common multiple of 6, 3, and 7 is 42, hence we can write: \(6a=3b=7c=42x\), for some number \(x\). So, \(a=7x\), \(b=14x\) and \(c=6x\). (1) \(ac=6b\) \(7x*6x=6*14x\); \(x^2=2x\); \(x=0\) or \(x=2\). Not sufficient. (2) \(5b=8a+4c\) \(5*14x=8*7x+4*6x\); \(70x=80x\); \(10x=0\); \(x=0\), hence \(a=b=c=0\) and \(a+b+c=0\). Sufficient.
Answer: B hi, Just a basic doubt.. while solving for statement 1  why can't we divide x from both sides. There by we will have a solution; x = 2. Do we always to take the possibility of a variable to be zero, if not mentioned explicitly. Thanks in advance



Math Expert
Joined: 02 Aug 2009
Posts: 7104

Re: M2721
[#permalink]
Show Tags
07 May 2016, 08:07
arunmandapaka wrote: Bunuel wrote: Official Solution:
If \(6a=3b=7c\), what is the value of \(a+b+c\)?
Given: \(6a=3b=7c\). The least common multiple of 6, 3, and 7 is 42, hence we can write: \(6a=3b=7c=42x\), for some number \(x\). So, \(a=7x\), \(b=14x\) and \(c=6x\). (1) \(ac=6b\) \(7x*6x=6*14x\); \(x^2=2x\); \(x=0\) or \(x=2\). Not sufficient. (2) \(5b=8a+4c\) \(5*14x=8*7x+4*6x\); \(70x=80x\); \(10x=0\); \(x=0\), hence \(a=b=c=0\) and \(a+b+c=0\). Sufficient.
Answer: B hi, Just a basic doubt.. while solving for statement 1  why can't we divide x from both sides. There by we will have a solution; x = 2. Do we always to take the possibility of a variable to be zero, if not mentioned explicitly. Thanks in advance yes, always get the variables on one side and solve for the variable if nothing is specified
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 09 Feb 2016
Posts: 5

Great problem!



Intern
Joined: 29 Oct 2016
Posts: 13

Re M2721
[#permalink]
Show Tags
30 May 2017, 17:08
I think this is a poorquality question. My answer was A. Please explain what is wrong with my understanding below.  We have 6a= 3b = 7c hence , 6a = 3b & 6a = 7c → b= 2a (1) and c = 6/7a (2). From this (1) and (2), we have b/c = 2a/ 6/7a = 14/6.  now a + b + c= a + 2a + 6/7a = 27/7 a. So we need to find the value of a.
From condition (1) ac=6b → a= 6b/c = 6 * 14/6 =14. Substitute this a = 14 to a+ b +c = 27/7 a we have a + +c = 54.
From condition (2), we can not find a, Hence only A is correct answer.
Please help. Thank you.



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: M2721
[#permalink]
Show Tags
30 May 2017, 20:15
Labmalo wrote: I think this is a poorquality question. My answer was A. Please explain what is wrong with my understanding below.  We have 6a= 3b = 7c hence , 6a = 3b & 6a = 7c → b= 2a (1) and c = 6/7a (2). From this (1) and (2), we have b/c = 2a/ 6/7a = 14/6.  now a + b + c= a + 2a + 6/7a = 27/7 a. So we need to find the value of a.
From condition (1) ac=6b → a= 6b/c = 6 * 14/6 =14. Substitute this a = 14 to a+ b +c = 27/7 a we have a + +c = 54.
From condition (2), we can not find a, Hence only A is correct answer.
Please help. Thank you. The question is flawless. The fact that you did no understood it does not mean that it's of poor quality. Your doubt is addressed in a post above as well as in the solution itself. (1) gives TWO sets a = b = c = 0 or a = 14, b = 28, and c = 12.
_________________
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
Status: All our dreams can come true, if we have the courage to pursue them
Joined: 03 Jul 2015
Posts: 23
Location: India
Concentration: Technology, Finance
WE: Information Technology (Computer Software)

Re: M2721
[#permalink]
Show Tags
05 Oct 2018, 15:53
This is a highquality trap question. Many people just cancel out the variable in case (1) and end up marking D as answer. Thanks Bunuel.



Manager
Joined: 29 May 2017
Posts: 127
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability

Re: M2721
[#permalink]
Show Tags
07 Oct 2018, 04:56
like most questions from Bunuel, this tests your core understanding of the concept and the assumptions that go into those concepts. In this case, exclusion of the possibility that a>0 On a side note, i did think of using the LCM but had no idea what will i do with it. this question has showed me how to!










