Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 11 May 2013
Posts: 8

If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
13 Jul 2013, 22:06
5
This post received KUDOS
20
This post was BOOKMARKED
Question Stats:
28% (01:47) correct 72% (01:56) wrong based on 876 sessions
HideShow timer Statistics
If 5a=9b=15c, what is the value of a+b+c? (1) 3ca=5c3b (2) 6cb=10a *Note  my answer is different from the official answer. I'm posting it here to confirm whether I'm correct or not.
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 43853

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
13 Jul 2013, 22:30
9
This post received KUDOS
Expert's post
9
This post was BOOKMARKED
If 5a=9b=15c, what is the value of a+b+c?Given: \(5a=9b=15c\) > least common multiple of 5, 9, and 15 is 45 hence we can write: \(5a=9b=15c=45x\), for some number \(x\) > \(a=9x\), \(b=5x\) and \(c=3x\). (1) 3ca=5c3b > \(9x9x=15x15x\) > \(0=0\) (this means that ANY appropriate values of a, b, and c satisfy the given statement). Not sufficient. (2) 6cb=10a > \(6*3x*5x=10*9x\) > \(90x^2=90x\) > \(x=0\) or \(x=1\). Not sufficient. (1)+(2) \(x=0\) or \(x=1\), thus \(a=b=c=0\) (for \(x=0\)) > \(a+b+c=0\) OR \(a=9\), \(b=5\), \(c=3\) (for \(x=1\)) > \(a+b+c=17\). Not sufficient. Answer: E. 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



Intern
Joined: 11 May 2013
Posts: 8

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
13 Jul 2013, 23:51
1
This post received KUDOS
Thanks Bunnuel.
My answer was B.
Using the original question, I solved for a:
5a = 9b a=9b/5
Then I substituted a into statement 2:
6cb = 10a 6cb = 10(9b/5) 6c = 90/5 30c = 90 c = 3
Once I have c , I calculated for a and b:
5a = 15(3) a = 45/5 a = 9
9b = 15(3) b = 5
a+b+c = 17



Math Expert
Joined: 02 Sep 2009
Posts: 43853

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
14 Jul 2013, 00:12



Intern
Joined: 04 Jul 2013
Posts: 2

Re: If 5a = 9b = 15c, what is the value of a + b + c? [#permalink]
Show Tags
21 Aug 2013, 20:12
We have from question that a=3c, 3b=5c, 5a=9b
Statement 1
3c  a = 5c  3b is the same as 3ba=2c, substitute a with 3c, we get 5c=3b. Hence Statement 1 is Not Sufficient.
Statement 2
6cb = 10a is the same as 6cb = 30c, Dividing both sides with 3c gives 2b = 10 and b = 5
With the value of b we can find that c = 3 and a = 9.
Hence statement 2 is Sufficient.
Thus the answer, B.



Math Expert
Joined: 02 Sep 2009
Posts: 43853

Re: If 5a = 9b = 15c, what is the value of a + b + c? [#permalink]
Show Tags
22 Aug 2013, 00:55
atewari wrote: We have from question that a=3c, 3b=5c, 5a=9b
Statement 1
3c  a = 5c  3b is the same as 3ba=2c, substitute a with 3c, we get 5c=3b. Hence Statement 1 is Not Sufficient.
Statement 2
6cb = 10a is the same as 6cb = 30c, Dividing both sides with 3c gives 2b = 10 and b = 5
With the value of b we can find that c = 3 and a = 9.
Hence statement 2 is Sufficient.
Thus the answer, B. The correct answer is E, not B. Check here: if5a9b15cwhatisthevalueofabc155926.html#p1246081 and here: if5a9b15cwhatisthevalueofabc155926.html#p1246110Hope it helps.
_________________
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



Director
Joined: 23 Jan 2013
Posts: 601

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
22 Aug 2013, 09:38
If 5a=9b=15c, what is the value of a+b+c?
(1) 3ca=5c3b (2) 6cb=10a
*Note  my answer is different from the official answer. I'm posting it here to confirm whether I'm correct or not.[/quote]
Statement 1: insufficient because having infinitely many solutions Statement 2: 6cb=10a means that 6cb=18b and 6cb=30c, so cb=3b and cb=5c c=3b/b=3 and b=5c/c=5 providing that c and b are not equal to 0. So I think ambiguity with 0 is resolved and a=9 so sum is 17. Sufficient



Math Expert
Joined: 02 Sep 2009
Posts: 43853

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
22 Aug 2013, 09:41



Manager
Status: Persevering
Joined: 15 May 2013
Posts: 217
Location: India
Concentration: Technology, Leadership
GMAT Date: 08022013
GPA: 3.7
WE: Consulting (Consulting)

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
24 Aug 2013, 04:57
OA is E; As correctly pointed out by bunuel You cannot simply reduce an expression ab=bc does not imply that a=c, as it is perfectly possible for b to be zero and var a might not be equal to var c.
_________________
It's one thing to get defeated, but another to accept it.



Senior Manager
Joined: 07 Sep 2010
Posts: 326

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
24 Aug 2013, 06:01
Bunuel wrote: (1)+(2) \(x=0\) or \(x=1\), thus \(a=b=c=0\) (for \(x=0\)) > \(a+b+c=0\) OR \(a=9\), \(b=5\), \(c=3\) (for \(x=1\)) > \(a+b+c=17\). Not sufficient.
Answer: E.
Hope it's clear.
Hi Bunuel, When combining St 1 and St2, isn't the only acceptable solution is when x=0, since x=0 is common to both statements. How x=1 validates both the statements? Pls clarify?
_________________
+1 Kudos me, Help me unlocking GMAT Club Tests



Math Expert
Joined: 02 Sep 2009
Posts: 43853

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
25 Aug 2013, 06:29
imhimanshu wrote: Bunuel wrote: (1)+(2) \(x=0\) or \(x=1\), thus \(a=b=c=0\) (for \(x=0\)) > \(a+b+c=0\) OR \(a=9\), \(b=5\), \(c=3\) (for \(x=1\)) > \(a+b+c=17\). Not sufficient.
Answer: E.
Hope it's clear.
Hi Bunuel, When combining St 1 and St2, isn't the only acceptable solution is when x=0, since x=0 is common to both statements. How x=1 validates both the statements? Pls clarify? The part you are quoting gives two examples: \(a=b=c=0\) \(a=9\), \(b=5\), \(c=3\)
_________________
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: 14 Aug 2005
Posts: 82

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
25 Aug 2013, 19:11
Bunuel wrote: jabronyo wrote: Thanks Bunnuel.
My answer was B.
Using the original question, I solved for a:
5a = 9b a=9b/5
Then I substituted a into statement 2:
6cb = 10a 6cb = 10(9b/5) 6c = 90/5 30c = 90 c = 3
Once I have c , I calculated for a and b:
5a = 15(3) a = 45/5 a = 9
9b = 15(3) b = 5
a+b+c = 17 The problem with your solution is that you cannot reduce 6cb = 10(9b/5) by b. Doing so you exclude b=0 case: 6cb = 10(9b/5) > cb=3b > b(c3)=0 > b=0 or c=3. Hope it's clear. I made the same mistake! Thanks Brunel for pointing it out
_________________
One Last Shot



NonHuman User
Joined: 09 Sep 2013
Posts: 13815

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
30 Aug 2014, 07:44
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 22 Jan 2014
Posts: 139
WE: Project Management (Computer Hardware)

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
31 Aug 2014, 02:27
jabronyo wrote: If 5a=9b=15c, what is the value of a+b+c?
(1) 3ca=5c3b (2) 6cb=10a
*Note  my answer is different from the official answer. I'm posting it here to confirm whether I'm correct or not. My take is E. 5a=9b=15c LCM(5,9,15) = 45. => a = 9x, b = 5y, and c = 3z 1) 3ca=5c3b => 6z = 15y9x or 2z = 5y  3x y and x must be odd for LHS to be even. so multiple solutions exist. 2) 6cb = 10a 6*5y*3z = 10*9x x = yz x=y=z=0 or x=y=z=1 not sufficient. 1)+2) x=y=z=0 or x=y=z=1 not sufficient. Hence, E.
_________________
Illegitimi non carborundum.



Intern
Joined: 03 Jul 2014
Posts: 34
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10172014
GPA: 4
WE: Analyst (Insurance)

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
04 Sep 2014, 17:45
Hi all, My answer is E. Given: 5a = 9b = 15c to find: a+b+c Let us suppose 5a = 9b = 15c = K (some constant) Therefore, a= K/5, b = K/9, and c = K/15 a+b+c = K/5 + K/9 + K/15 = 17K/45 Now we have to find K statement 1 : 3ca = 5c3b 3*(K/15)(K/5) = 5*(K/15)3*(K/9) This reduces to 0=0 hence, statement 1 alone is not sufficient statement 2: 6cb = 10a I'll write this as 6cb10a = 0 6*(K/15)*(K/9)10(K/5) = 0 => 2*(K^2)/45  2*K = => 2K(K/45  1) = either K = 0 or K = 45 so a+b+c = 17K/45 = 0 or 17 hence, statement 2 alone is not sufficient statement 1 and statement 2 together will not suffice because statement 1 reduces to 0. Hence, the correct answer is E.  Kudos if this helps



Intern
Joined: 11 May 2015
Posts: 1

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
16 May 2015, 05:17
Here's the simplest way that I've found to solve the problem.
(1) 3c  a = 5c 3b Simplifies to 3b = 2c + a Multiply equation by 3 9b = 6c + 3a Substitute 5a for 9b 5a = 6c + 3a Simplify 2a = 6c 5a=15c, so we 2a always equals 6c 6c = 6c This expression is always true, so (1) does not help us figure out a+b+c at all.
(2) 3cb = 5a I converted this equation to look more similar to the question. 1/5 (15c) 1/9 (9b) = 5a 1/5 (5a) 1/9 (5a) = 5a 1/45 (25a^2) = 5a 1/9 (a^2) = a 1/9a^2  a = 0 a(1/9a  1) = 0 a = 0, 9. NOT SUFFICIENT
Answer is E. Many of the other strategies to get E are correct, but I would not think to do them on the test. (I guess I need to keep studying) This way is just basic basic algebra.



Current Student
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If 5a = 9b = 15c , what is the value of : [#permalink]
Show Tags
19 Dec 2015, 04:56
sara86 wrote: If 5a = 9b = 15c , what is the value of a+ b + c ?
(1) 3c  a = 5c  3b
(2) 6cb = 10a Follow posting guidelines (link in my signatures) and do not disable the timer.As for your question, you are given 5a = 9b = 15c > 5a = 9b = 15c = k > a = k/5, b=k/9 and c=k/15. Thus, a+b+c = k *(some fixed number). Thus for determining the sufficiency, you need to find 1 unique value of 'k'. Per statement 1, 3c  a = 5c  3b > substitute the values of a,b,c from above, you will see that you get 0=0 thus this means that this statement is NOT sufficient to find the value of 'k'. Per statement 2, 6cb = 10a > substitute the values of a,b,c you get : k^2=45*k > k = 0 or k=45. Thus you still do not know 1 unique value of 'k'. Combining the 2 statements, you still get k=0 or k=45, making E the correct answer. Hope this helps.



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4897
GPA: 3.82

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
21 Dec 2015, 21:05
If 5a=9b=15c, what is the value of a+b+c? (1) 3ca=5c3b (2) 6cb=10a When you modify the original condition and the question, divide 5a=9b=15c with 45. You get a/9=b/5=c/3 and suppose it k. That is, a/9=b/5=c/3=k and from a=9k, b=5k, c=3k, there are 4 variables(a,b,c,k) and 3 equations(a=9k, b=5k, c=3k), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. In 1), when substituting a,b,c, it becomes 3(3k)9k=5(3k)3(5k) and 0=0, which is satisfied with all k. So it is not unique and therefore not sufficient. In 2) when substituting a,b,c, it becomes 6(3k)(5k)=10(9k) and k^2=k, k(k1)=0, k=0,1 where the value of k is not unique and therefore not sufficient. Even in 1) & 2), 1) k=all numbers 2) k=0,1, which is not unique and not sufficient. Therefore the answer is E. > For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Find a 10% off coupon code for GMAT Club members. “Receive 5 Math Questions & Solutions Daily” Unlimited Access to over 120 free video lessons  try it yourself See our Youtube demo



Manager
Joined: 07 May 2015
Posts: 102

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
02 Jan 2016, 10:14
Bunuel wrote: If 5a=9b=15c, what is the value of a+b+c?
Given: \(5a=9b=15c\) > least common multiple of 5, 9, and 15 is 45 hence we can write: \(5a=9b=15c=45x\), for some number \(x\) > \(a=9x\), \(b=5x\) and \(c=3x\).
(1) 3ca=5c3b > \(9x9x=15x15x\) > \(0=0\) (this means that ANY appropriate values of a, b, and c satisfy the given statement). Not sufficient.
(2) 6cb=10a > \(6*3x*5x=10*9x\) > \(90x^2=90x\) > \(x=0\) or \(x=1\). Not sufficient.
(1)+(2) \(x=0\) or \(x=1\), thus \(a=b=c=0\) (for \(x=0\)) > \(a+b+c=0\) OR \(a=9\), \(b=5\), \(c=3\) (for \(x=1\)) > \(a+b+c=17\). Not sufficient.
Answer: E.
Hope it's clear. Hi Bunnel, Can you please help me understand why A is not sufficient. With the solution you have, it comes out that a=b=c=0 so why is a+b+c = 0 wrong. Thanks in advance!



Math Expert
Joined: 02 Sep 2009
Posts: 43853

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
Show Tags
03 Jan 2016, 09:47
neeraj609 wrote: Bunuel wrote: If 5a=9b=15c, what is the value of a+b+c?
Given: \(5a=9b=15c\) > least common multiple of 5, 9, and 15 is 45 hence we can write: \(5a=9b=15c=45x\), for some number \(x\) > \(a=9x\), \(b=5x\) and \(c=3x\).
(1) 3ca=5c3b > \(9x9x=15x15x\) > \(0=0\) (this means that ANY appropriate values of a, b, and c satisfy the given statement). Not sufficient.
(2) 6cb=10a > \(6*3x*5x=10*9x\) > \(90x^2=90x\) > \(x=0\) or \(x=1\). Not sufficient.
(1)+(2) \(x=0\) or \(x=1\), thus \(a=b=c=0\) (for \(x=0\)) > \(a+b+c=0\) OR \(a=9\), \(b=5\), \(c=3\) (for \(x=1\)) > \(a+b+c=17\). Not sufficient.
Answer: E.
Hope it's clear. Hi Bunnel, Can you please help me understand why A is not sufficient. With the solution you have, it comes out that a=b=c=0 so why is a+b+c = 0 wrong. Thanks in advance! Did we get that a=b=c=0? NO. Given that 5a=9b=15c, 3ca=5c3b would be true for ANY a, b, and c. Try several numbers to check.
_________________
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




Re: If 5a=9b=15c, what is the value of a+b+c?
[#permalink]
03 Jan 2016, 09:47



Go to page
1 2
Next
[ 23 posts ]



