Question

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 $(a + b + c)$?

Accepted Answer

C. Given: $a : b = 3 : 4$ $b : c = 2 : 1 = 4 : 2$ So $a : b : c = 3 : 4 : 2$. Sum $a + b + c = 3k + 4k + 2k = 9k$. Therefore, $(a + b + c)$ must be a multiple of 9. Checking options for divisibility by 9: - 201: sum of digits = 3 (not divisible) - 205: sum of digits = 7 (not divisible) - 207: sum of digits = 9 (divisible by 9) - 210: sum of digits = 3 (not divisible) Hence, 207 is a possible value.

Ratio of Positive Integers a, b, c

Explanation

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