Data Sufficiency

A group of 580 people participated in a survey. Each of these people indicated that they had either heard of brand A soda or had not heard of brand A soda, and each of these people indicated that they had either heard of brand B soda or had not heard of brand B soda. How many of the people surveyed indicated that they had heard of brand A soda and had not heard of brand B soda?

(1) There were 226 people who indicated that they had heard of exactly one of the two brands of soda.

(2) There were 187 people who indicated that they had not heard of either brand soda and there were 281 people who indicated that they had heard of brand B soda.

OA is B

I tried the overlapping set formula and chose C, but I guess that was unnecessary. Another explanation would be appreciated!

sdotgarcia wrote:A group of 580 people participated in a survey. Each of these people indicated that they had either heard of brand A soda or had not heard of brand A soda, and each of these people indicated that they had either heard of brand B soda or had not heard of brand B soda. How many of the people surveyed indicated that they had heard of brand A soda and had not heard of brand B soda?

(1) There were 226 people who indicated that they had heard of exactly one of the two brands of soda.

(2) There were 187 people who indicated that they had not heard of either brand soda and there were 281 people who indicated that they had heard of brand B soda.

OA is B

I tried the overlapping set formula and chose C, but I guess that was unnecessary. Another explanation would be appreciated!

This is an EITHER/OR group problem.
Every person had EITHER heard of A OR had not heard of A.
Every person had EITHER heard of B OR had not heard of B.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data:

In the grid above, the entries in any given row or column must add up to the TOTAL of that row or column.
The question stem asks for the number of people who had heard of A but had not heard of B (represented by the question mark).

Statement 1: There were 226 people who indicated that they had heard of exactly one of the two brands of soda.
Case 1:

In this case, the number of people who had heard of A but had not heard of B = 100.

Case 2:

In this case, the number of people who had heard of A but had not heard of B = 126.

Since the number of people who had heard of A but had not heard of B can be different values, INSUFFICIENT.

Statement 2: There were 187 people who indicated that they had not heard of either brand soda and there were 281 people who indicated that they had heard of brand B soda.
The following grid is yielded:

According to the resulting grid, the number of people who had heard of A but had not heard of B = 112.
SUFFICIENT.

The correct answer is B.

Thanks yet again Mitch!!