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

Question

https://gmatclub.com/forum/download/file.php?id=51646 The table above shows the responses of 100 consumers to a taste test involving two colas. Each of the 100 consumers responded "Above Average," "Average," or "Below Average" when asked their opinion regarding the taste of Cola A and the taste of Cola B. How many of the 100 people in the poll responded Below Average for both colas? (1) Fifteen consumers responded "Above Average" for both colas. (2) Forty consumers did not respond "Below Average" for either cola. Are You Up For the Challenge: 700 Level Questions Princeton.png

MahmoudFawzy · Answer

The given can be simplified into the following info: 
raters for Cola A as average or above = 65
raters for Cola A below average = 35
raters for Cola B as average or above = 70
raters for Cola B below average = 30

From statement (1), raters for Both as above average = 15
this is  sufficient  because we can't know the number of raters for both as average

From statement (2),  raters for Both as average or above =  40  
this is just what is needed to find the missing numbers in the table.
then   the number of raters for Both as below average = 5  
 B

Subliminal · Answer

The number of people who responded to the survey is 100. This is important information.
We can also understand that a person cannot respond with more than one type of response, but can respond about 2 drinks.

Statement I alone - Since we don't know how many people voted for average or below average, statement I is insufficient.

Statement II alone - Since 40 customers did not respond below average to cola, it means 60 responded below average to cola. We can draw a Venn diagram considering 60 as the total respondents who responded below average to cola. 
From the Venn diagram, we can find out the number of people who responded below average to both colas as 5

Correct answer option is B, in my opinion.
Cheers!

MI83 · Answer

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.

BrentGMATPrepNow · Answer

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: 
 https://i.imgur.com/D0ahAhG.png 
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.
 https://i.imgur.com/IKbz6jG.png 
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:
 https://i.imgur.com/WUjSSDU.png

We now have enough information to complete the matrix:
 https://i.imgur.com/YMLyguu.png

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:
 https://www.youtube.com/watch?v=jK-tiBrrf04

EXTRA PRACTICE QUESTION
 https://www.youtube.com/watch?v=DsbPUSH_Wu4

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

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