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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

In a group of 60 traders in a market, 35 deal in cloth, 28 deal in grain, and 8 deal in neither. How many traders deal in both cloth and grain?

The answer is 11. Traders dealing in at least one commodity number 60 minus 8, which is 52. Adding the cloth and grain dealers gives 63, and the excess of 63 over 52 is the overlap, so 11 traders deal in both cloth and grain.

  1. A11Correct
  2. B19
  3. C3
  4. D16

Explanation

Traders dealing in at least one = 60 − 8 = 52. By n(C ∪ G) = n(C) + n(G) − n(C ∩ G), 52 = 35 + 28 − x, so x = 63 − 52 = 11. Choosing 19 comes from forgetting to remove the 8 who deal in neither (63 − 44... or similar mistakes), which gives a wrong overlap.

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