The table above shows the responses of 100 consumers to a taste test

OFFICIAL EXPLANATION
This is a Value Data Sufficiency question, so use the Pieces of the Puzzle approach to assess the question. Determine "What is known" from the question stem and "What is needed" from the statements to answer the question. Begin by determining "What is known." The question stem provides the ratings for each cola by the 100 people polled. Since this is a problem about groups, determine whether to use the group equation or the group grid. The presence of the word both indicates that the group formula is appropriate here. The group formula is Total = Group 1 + Group 2 – Both + Neither. In this case, let Group 1 represent people who responded “Below Average” to Cola A, which is 35 people according to the table, and let Group 2 represent people who responded “Below Average” to Cola B, which is 30 people. The Total is all 100 people surveyed. Next, figure out “What is needed.” To answer the question, the statement(s) must provide sufficient information to solve for the number of people who responded “Below Average” for both Cola A and Cola B. The missing piece from the group equation is Neither, or the number of people who didn’t rate either Cola as “Below Average.” Evaluate the statements one at a time.

Evaluate Statement (1). Statement (1) says that 15 consumers responded “Above Average” for both colas. Anyone who responded “Above Average” for both colas did not respond "Below Average" for either cola. This is a portion of the number of consumers who responded "Below Average" for neither cola. However, consumers who responded "Average" for both colas or who responded "Average" for one cola and "Above Average" for the other cola also responded "Below Average" for neither cola. When different numbers that satisfy a statement yield different answers to the question, the statement is insufficient. So, write down BCE.

Now, evaluate Statement (2). Statement (2) says that 40 consumers did not respond “Below Average” for either cola. Plugging In the information from the question stem into the group formula, Total = Group 1 + Group 2 − Both + Neither, yields 100 = 35 + 30 − Both + Neither. Statement (2) provides the information that Neither = 40, which can be inserted into the group formula to get 100 = 35 + 30 − Both + 40. Add Both to each side and subtract 100 from each side to get Both = 5, which is the answer to the question in the question stem. Therefore Statement (2) is sufficient, so eliminate choice C and choice E.

The correct answer is choice B.

Let's solve this question using the Double Matrix method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
For this particular question, we only care about the people who responded Below Average for both colas
So, we can combine the people who responded average and above-average to get the following:

I have placed that star in the box representing the people who responded Below Average for both colas.

Target question: What is the value in the top left box (denoted by a star)?


Statement 1: Fifteen consumers responded "Above Average" for both colas.
This information belongs in the bottom right box of the double matrix.

However, since we have combined the people who responded average and above-average, we still don't know how many people responded "Average"
As such, we don't have enough information to determine the value in the bottom right box, which means there's no way to complete the rest of the matrix.
Statement 1 is NOT SUFFICIENT

Statement 2: Forty consumers did not respond "Below Average" for either cola.
We can add this information to our matrix to get:


We now have enough information to complete the matrix:


So, the answer to the target question is 5 people responded Below Average for both colas
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video:


EXTRA PRACTICE QUESTION

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