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# m06 q14

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Manager
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04 Jan 2010, 19:34
What is the sum of a, b, and c?

1. a:b:c = 3:4:7

2. c-a = 12

Statements (1) and (2) combined are sufficient. Combining the two gives us the ratio between c and a. Thus if the difference between c and a is 12 and the difference in proportion is 4, then each of the proportions needs to be multiplied by 3 or (3+4+7)*3 = 42.

Can someone explain to me why you multiply by 3? I am not following the logic on this one.
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Manager
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04 Jan 2010, 22:49
phillypointgod21 wrote:
What is the sum of a, b, and c?

1. a:b:c = 3:4:7

2. c-a = 12

Statements (1) and (2) combined are sufficient. Combining the two gives us the ratio between c and a. Thus if the difference between c and a is 12 and the difference in proportion is 4, then each of the proportions needs to be multiplied by 3 or (3+4+7)*3 = 42.

Can someone explain to me why you multiply by 3? I am not following the logic on this one.

Philly,
I'll try to explain.
3, 4, 7 are ratio( of a number) . Let the original number be x.
So a = 3/14 of x; b = 4/14 of x and c = 7/14 of x.

Using stmt 2, c - a = 12 and above, we get (7/14 - 3/14)x = 12. Solving, 4x = 12*14, so x = 3* 14.
= > x = 42.
Sum has to be * by 3. ( ( 3+4+7) * 3)
I hope now its clear why we multiply by 3.

Cheers
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05 Jan 2010, 10:45
Though aditya has given a good algebric explanation,here is another take.I hope it will also help u understand!

when u say a:b:c=3:4:7,it doesn't mean values of a,b,c are 3,4,7...It can be 3,4,7 or 6,8,14 or 9,12,21 and so on..It just means the simplest ratio between terms are in 3:4:7.

So stmt (1) alone is not sufficient.

c-a=12 doesnt tell us their values.So stmt(2) alone is not suffiient.

Combing these two, if we assume a,b,c are 9,12,21.these values satisfy both stmts, hence assumption is correct.

We get a,b,c as 9,12,21 by multiplying the ratio by 3.
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05 Jan 2010, 21:16
Thanks guys - both entries are helpful!
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Re: m06 q14   [#permalink] 05 Jan 2010, 21:16
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# m06 q14

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