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# CAT 2017 [slot 2] Question with solution 11

Question 45:
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)?
1. 201
2. 205
3. 207
4. 210
Option: 3
Explanation:

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.

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