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A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is

A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is Correct Answer 43

Calculation:

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Let the number of players who can play all three games be x.

The number of players only play football = 144 - (58 - x) - (x) - (63 - x)

⇒ 23 + x

The number of players only play tennis = 123 - (58 - x) - (x) - (25 - x)

⇒ 40 + x

The number of players only play cricket = 132 - (25 - x) - (x) - (63 - x)

⇒ 44 + x

The total number of players = 256

⇒ 144 + 40 + x + 25 - x + 44 + x = 256

⇒ 253 + x = 256

⇒ x = 3

The number of players who can only play tennis = 40 + x

⇒ 40 + 3

⇒ 43

∴ The number of players who can only play tennis is 43.

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