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)?

• A. 201
• B. 205
• C. 207
• D. 210

Answer 1

Answer: (C)

207

Answer 2

The correct answer is (C):
a : b = 3 : 4 and b : c = 2 : 1
Multiplying the second ratio by 2, we have
a : b = 3 : 4
b : c = 4 : 2
Therefore, a : b : c = 3 : 4 : 2.
⇒ a = 3k, b = 4k, c = 2k.
Since a, b and c are positive integers, their sum should be 9k, a positive integer.
From the options, only choice (3), which is 207, is a multiple of 9.