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The Venn diagram below illustrates the sports preferences stated by a group of 100 college students. These students play one of the three games given below and 5 of them play all three games. These three sports are: Football (A), Tennis (B) and Cricket (C). Based on the diagram, how many students only like playing tennis and football?

The Venn diagram below illustrates the sports preferences stated by a group of 100 college students. These students play one of the three games given below and 5 of them play all three games. These three sports are: Football (A), Tennis (B) and Cricket (C). Based on the diagram, how many students only like playing tennis and football? Correct Answer 38

Given:

1) Total students in college = 100

2) Number of students who play all three games = 5

3) Number of students who play only Football (A) = 13

4) Number of students who play only Tennis (B) = 12

5) Number of students who play only Cricket (C) = 10

6) Number of students who play both Football and Cricket = 10

7) Number of students who play both Tennis and Cricket = 12 

Concepts used :

Used of Venn diagram.

[ alt="F1 Prashant Shraddha 16.02.2021 D6" src="//storage.googleapis.com/tb-img/production/21/02/F1_Prashant_Shraddha_16.02.2021_D6.png" style="width: 210px; height: 156px;">

Calculation;

Let the number of students who only like playing Tennis and Football be  x,

From the above figure: We can write,

Total number of students,

100 = 13 + x + 5 + 10 + 12 + 12 + 10

100 = 62 + x

x = 100 - 62

x = 38.

Hence, the correct answer is "38".

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