BTGmoderatorLU wrote:Source: Princeton Review



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.

The OA is B

Let's take each statement one by one.

1) Fifteen consumers responded "Above Average" for both colas.

This is not going to help. From this information, we can get to know how many consumers responded "Above Average" for either cola, which is equal to 20 + 40 - 15 = 45. However, we cannot know how many of the 100 people in the poll responded Below Average for both colas. Insufficient.

2) Forty consumers did not respond "Below Average" for either cola.

=> 60 consumers responded "Below Average" for either cola.

Thus, no. of consumers who responded "Below Average" for both colas = 35 + 30 - 60 = 5. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorLU wrote: ↑

Sat Nov 23, 2019 3:30 am

Source: Princeton Review



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.

The OA is 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: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent