If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2 : 1, then which one of the following is a possible value of (a + b + c)?

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207 — Easy Merge the two pairwise ratios into a single $a:b:c$. Their sum is then a fixed multiple of an integer, so the answer must be that multiple — only one option qualifies. 1 Combine the ratios. $a:b=3:4$ and $b:c=2:1$. Make $b$ common (scale the second by $2$ to $4:2$). $$\begin{aligned} &a:b:c=3:4:2 \end{aligned}$$ 2 Form the sum. Write $a=3k,\ b=4k,\ c=2k$ for a positive integer $k$. $$\begin{aligned} &a+b+c=3k+4k+2k=9k \end{aligned}$$ 3 Match the options. The sum must be a multiple of $9$. C

CAT 2017 Slot 2 — QA Question 11

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