For this question we should avoid the temptation of testing values, since that strategy only yields definitive results when the correct answer is D. Otherwise, we're left wondering whether we've tested enough values.

Given: When x is divided by 9, the remainder is 4.
In other words, x is 4 greater than some of multiple of 9.
So we can write: x = 9k + 4 (for some integer k)

So, 3x = 3(9k + 4) = 27k + 12
Now recognize that we can take the expression 27k + 12 and rewrite it as follows...
27k + 12 = 27k + 9 + 3 = 9(3k + 1) + 3

Since 9(3k + 1) is a multiple of 9, it must also be true that 9(3k + 1) + 3 is 3 greater than some multiple of 9.
So, if we take 9(3k + 1) + 3 and divide it by 9, the remainder will be 3.

So we get:
QUANTITY A: 3
QUANTITY B: 4

Answer: B