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CAT 2019 Slot 1 · Quantitative Ability · Medium · Set theory

This is a medium Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Set theory. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

  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.

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