Venn Diagram of Sports Played

CAT 2019 Slot 1 · QA · Medium · Set theory

All CAT 2019 Slot 1 questionsMore Set theory questionsAll CAT QA

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. A.

    32

  2. B.

    43

  3. C.

    38

  4. D.

    45

Answer

B

Explanation

Let F,T,CF, T, C be the sets of members playing Football, Tennis, and Cricket. ∣F∪T∪C∣=∣F∣+∣T∣+∣C∣−(∣F∩T∣+∣T∪C∣+∣F∩C∣)+∣F∩T∩C∣|F \cup T \cup C| = |F| + |T| + |C| - (|F \cap T| + |T \cup C| + |F \cap C|) + |F \cap T \cap C| 256=144+123+132−(58+25+63)+x  ⟹  256=399−146+x=253+x  ⟹  x=3256 = 144 + 123 + 132 - (58 + 25 + 63) + x \implies 256 = 399 - 146 + x = 253 + x \implies x = 3. Only tennis =∣T∣−∣F∩T∣−∣T∩C∣+∣F∩T∩C∣=123−58−25+3=43= |T| - |F \cap T| - |T \cap C| + |F \cap T \cap C| = 123 - 58 - 25 + 3 = 43.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace