CAT 2017 Slot 2 — QA Question 11
RatioEasy
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)?
Answer & solution
- A
201
- B
205
207
- D
210
Solution
a : b = 3 : 4
b : c = 2 : 1
To get a common ratio we take LC.M (2, 4) = 4
So, we multiply each of b and c by 2
Hence, ratio of b : c = 4 : 2
∴ Ratio of a : b : c = 4 : 2
Now let a = 3x, b = c = 3 : 4 : 2
So a + b + c = 3x + 4x + 2x = 9x
As, a, b and c are all positively integers, it implies that the sum of a, b and c will be a positive integer and a multiple of 9.
Out of the given options, only 207 i.e, option (c) is a multiple of 9.
Hence, option (c).