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What is the ratio of a:b:c?

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What is the ratio of a:b:c?

by melguy » Mon Aug 05, 2013 4:21 am
If a,b and c are positive integers. What is the ratio of a:b:c?

1) b = 4 and ac = 21.

2) a/c = 3/7 and c/b = 7/4

Can i put statement 2 as

3/7c : 4/7c : c (and hence making it sufficient?)

Thanks
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by Brent@GMATPrepNow » Mon Aug 05, 2013 5:42 am
melguy wrote:If a,b and c are positive integers. What is the ratio of a:b:c?

1) b = 4 and ac = 21.

2) a/c = 3/7 and c/b = 7/4

Target question: What is the ratio of a:b:c?

Statement 1: b = 4 and ac = 21
There are several sets of values that meet this condition. Here are two:
Case a: a = 3, b = 4 and c = 7, in which case a:b:c = 3:4:7
Case b: a = 1, b = 4 and c = 21, in which case a:b:c = 1:4:21
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a/c = 3/7 and c/b = 7/4
a/c = 3/7 means that a:c = 3:7
c/b = 7/4 means that c:b = 7:4
Since both ratios have c = 7 in common, we can combine the ratios to get a:c:b = 3:7:4
Rearrange to get a:b:c = 3:4:7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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Brent
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by Brent@GMATPrepNow » Mon Aug 05, 2013 5:47 am
melguy wrote: Can i put statement 2 as

3/7c : 4/7c : c (and hence making it sufficient?)

Thanks
Yes, that also works.

Notice that, if a : b : c = 3/7c : 4/7c : c, then we can take the ratio on the right side and multiply all 3 terms by 7 to get the equivalent ratio 3:4:7

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by GMATGuruNY » Mon Aug 05, 2013 8:56 am
It should also be noted that -- like fractions -- ratios can be multiplied together.
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https://www.beatthegmat.com/is-alligatio ... 14121.html
https://www.beatthegmat.com/ds-1-t264883.html
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