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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram

In a group of 100 students at a Kolkata coaching centre, 52 study Costing, 48 study Accounts and 40 study Law. 20 study Costing and Accounts, 18 study Accounts and Law, 16 study Costing and Law, and 8 study all three. How many study at least one subject?

94 students study at least one subject. By the inclusion-exclusion rule, add the single-subject totals 52, 48 and 40 to get 140, subtract the pairwise overlaps totalling 54, and add back the 8 who study all three, giving 94.

  1. A94Correct
  2. B98
  3. C86
  4. D90

Explanation

Union = 52+48+40 - (20+18+16) + 8 = 140 - 54 + 8 = 94. The option 86 results from subtracting the triple overlap instead of adding it back (140-54-8=78 is not it, but 86 comes from 140-54 = 86 with the 8 omitted).

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