Explanation

In this question, the answer choices are friendly, round, numbers, so we can guess an answer choice and work it backwards to see whether it's correct.

We are looking for the difference in men and women after the addition, when the ratio is . This difference can be expressed as , where n is an integer. So the correct answer will be divisible by 3. That means that choice (D) is definitely out, because the digits in (D) don't sum to a number that is divisible by 3.

We can try choice (C). If (C) is correct, then the final difference is , , and the final numbers of men and women are men and women. In that case, prior to the additions, this means 214 women and 310 men. These are supposed to be in a ratio of 3 to 5, but isn't even divisible by 3. That means that answer choice (C) cannot be correct.

We can try (B). If (B) is correct, then the final difference is and . The men are and the women are in the final ratio. In this case, prior to additions, the men are 130 and the women are 78. Is 78 to 130 a ratio of 3 to 5? We try Working backward was successful in this case, so we have our correct answer.

Note that, if (B) hadn't been correct, we would be left with only (A) and (E) as possibilities, and we likely would have been able to choose one over the other by identifying whether we needed larger or smaller numbers than in choice (B).

The correct answer is (B).