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Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
13 Jul 2013, 22:30

7

This post received KUDOS

Expert's post

5

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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) 3c-a=5c-3b --> \(9x-9x=15x-15x\) --> \(0=0\) (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.

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
22 Aug 2013, 09:38

If 5a=9b=15c, what is the value of a+b+c?

(1) 3c-a=5c-3b (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

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

Expert's post

Temurkhon wrote:

If 5a=9b=15c, what is the value of a+b+c?

(1) 3c-a=5c-3b (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.

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

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
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.

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
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? _________________

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
25 Aug 2013, 06:29

Expert's post

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: \(a=b=c=0\) \(a=9\), \(b=5\), \(c=3\) _________________

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
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).

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Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
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 : 3c-a = 5c-3b 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 6cb-10a = 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

Re: If 5a=9b=15c, what is the value of a+b+c? [#permalink]
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.

gmatclubot

Re: If 5a=9b=15c, what is the value of a+b+c?
[#permalink]
16 May 2015, 05:17

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