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In a class of 95 students, all play at least one of the three games — snooker, chess and tennis. 42 students play snooker, 49 play tennis, and 43 play chess. The total number of students who play any and only two games is 29. 5 students play all the three games. The number of students who play only snooker and only chess is equal. 11 students play only snooker and tennis. 6 students play only snooker and chess. How many students play only tennis?

In a class of 95 students, all play at least one of the three games — snooker, chess and tennis. 42 students play snooker, 49 play tennis, and 43 play chess. The total number of students who play any and only two games is 29. 5 students play all the three games. The number of students who play only snooker and only chess is equal. 11 students play only snooker and tennis. 6 students play only snooker and chess. How many students play only tennis? Correct Answer 21

The least possible Venn diagram for the given information is as shown below :

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The total number of students in a class = 95 students.

⇒ Number of students play snooker = 42

⇒ Number of students play tennis = 49

⇒ Number of students play chess = 43

⇒ Number of students who play all three games = 5

GIven:

  • The total number of students who play any and only two games = 29.

⇒ Number of students play only snooker and tennis = 11

⇒ Number of students play only snooker and chess = 6

∴ Number of students play only tennis and chess = Total number of students who play any and only two games - (Number of students play only snooker and tennis + Number of students play only snooker and chess)

⇒ Number of students play only tennis and chess = 29 - (11 + 6)

⇒ Number of students play only tennis and chess = 29 - 17

→ Number of students play only tennis and chess = 12

⇒ Number of students who play only snooker = Number of students play snooker - (Number of students who play all three games + Number of students play only snooker and tennis + Number of students play only snooker and chess)

⇒ Number of students who play only snooker = 42 - (5 + 11 + 6)

⇒ Number of students who play only snooker = 42 - 22

⇒ Number of students who play only snooker = 20

⇒ The number of students who play only snooker and only chess is equal = 20

⇒ Number of students who play only tennis = Number of students play tennis - (Number of students who play all three games + Number of students play only tennis and chess + Number of students play only snooker and tennis)

⇒ Number of students who play only tennis = 49 - (5 + 12 + 11)

⇒ Number of students who play only tennis = 49 - 28

⇒ Number of students who play only tennis = 21

Hence, the correct answer is "21".

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