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CAT 2019 Quant Question with Solution 13

Question:
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

  1. 45
  2. 38
  3. 32
  4. 43
Show Answer

Correct Answer: Option: 4

Let the number of members playing all three games be x.

Given, that all the members play at least one of these three games, hence the union of these three sets = 256.

Therefore,

256 =144+123+132)-(58+25+63)+x

Or x = 3.

Fitting the numbers in the venn diagram, we get

Clearly, the number of members playing only tennis = 43.


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