Given: a : b = 3 : 4 and b : c = 2 : 1
Both ratios share the variable b.
To combine the ratios into one big ratio, we need to find a ratio that's equivalent to 2 : 1 so that both ratios share the same b-value.
If b : c = 2 : 1, we can multiply both sides of the given ratio by 2 to get the equivalent ratio: b : c = 4 : 2

We now have: a : b = 3 : 4 and b : c = 4 : 2

We can all combined ratios to get: a : b : c = 3 : 4 : 2

Since we're told a, b, c are three positive integers, we know that a + b + c must be a multiple of 3 + 4 + 2
In other words, a + b + c must be a multiple of 9

Useful property: A number is divisible by 9 if and only if, the sum of its digits is divisible by 9.

When we check the answer choices, only answer choice D is such that the sum of its digits is divisible by 9 (i.e., 2 + 0 + 7 = 9, which is divisible by 9)

Answer: D