Problem Solving

This is an overlapping sets problem, where we have two overlapping sets (Basketball vs. No Basketball and Hockey vs. No Hockey). When we have two overlapping sets, your best bet is to make a double matrix.



Then, we fill in what we know:



To answer the question, we need to find how many students play both basketball and hockey, which is the top left white cell.

In a double matrix, the top two cells in each column should add up to the total in the bottom cell in the column, and the leftmost two cells in each row should add up to the total in the rightmost cell in the row. This means that if we have two cells in one row or two cells in one columns, we can use that information in the table to fill in the third cell. Let's see what else we can determine in our table:



then



then finally



So 10 students play both basketball and hockey.

I thought I'd point out that Erika's Double Matrix technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- plays field hockey or does NOT play field hockey
- plays basketball or does NOT play basketball

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

AAPL wrote:In a group of students, 5 participate in no after school activities and 16 participate in basketball. If 15 participate in field hockey and the group contains 26 students, how many students participate in both field hockey and basketball?

A. 4
B. 5
C. 6
D. 10
E. 21

The OA is D.

I don't understand why that is the correct answer. Please, can any expert explain this PS question for me?

We can use the formula:

Total = Basketball + Field Hockey - Both + Neither

26 = 16 + 15 - B + 5

26 = 36 - B

B = 10

Answer: D