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Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or

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Bunuel
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Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or [#permalink] Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or   25 Jan 2022, 05:30
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76% (01:07) correct 24% (01:17) wrong based on 102 sessions
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Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or both. If four students play both sports and eight students play only tennis, how many students play only soccer?

A. 12
B. 14
C. 16
D. 18
E. 20
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Re: Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or [#permalink] Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or   29 Jan 2022, 23:46
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Bunuel
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Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or both. If four students play both sports and eight students play only tennis, how many students play only soccer?

A. 12
B. 14
C. 16
D. 18
E. 20


Bumping for discussion. Destroy this one and get Kudos for a correct solution!!!!

Total = 24,
Only Tennis = 8
Both = 4

Only Soccer = 24-8-4 = 12
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BrentGMATPrepNow
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Re: Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or [#permalink] Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or   21 Feb 2022, 18:13
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Bunuel
Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or both. If four students play both sports and eight students play only tennis, how many students play only soccer?

A. 12
B. 14
C. 16
D. 18
E. 20
One approach is to use 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).
Here, we have a population of students, and the two characteristics are:
- plays tennis or doesn't play tennis
- plays soccer or doesn't play soccer

So we can set up our Matrix as follows:

Important: Since every student plays tennis, soccer or both, we can conclude that there are ZERO students that play neither tennis nor soccer. That's why we have 0 in the bottom right corner.

Given: 4 students play both sports and 8 students play only tennis.
We can add this to the diagram:


Question: How many students play only soccer?
At this point we have accounted for 12 of the 24 students, which means the remaining 12 must be placed in the last remaining box (which represents the number of students that play soccer but not tennis)

Answer: A

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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Re: Each of the 24 students in Mr. Martins class plays tennis, soccer, or [#permalink] Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or   18 Aug 2023, 03:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Each of the 24 students in Mr. Martins class plays tennis, soccer, or [#permalink]
18 Aug 2023, 03:52
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