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

In a class of 80 students, 50 passed Accounting, 45 passed Law and 40 passed Economics. Every student passed at least one subject, and exactly 10 students passed all three. If the number who passed exactly two subjects is x, what is x?

The answer is 35. Inclusion-exclusion gives the sum of pairwise overlaps as 135 + 10 − 80 = 65. Each triple-pass student is counted in all three pairs, adding 30, so those passing exactly two subjects number 65 − 30 = 35.

  1. A25
  2. B35Correct
  3. C45
  4. D55

Explanation

With everyone passing at least one, 80 = 135 − (sum of pairwise overlaps) + 10, so the pairwise sum is 65. Let x be exactly-two count; each pairwise overlap includes the triple 10 students, so the pairwise sum = x + 3×10 = x + 30. Thus x = 35. Check: exactly one = 80 − 35 − 10 = 35, and subject totals: 35 + 2×35 + 3×10 = 135, which matches.

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