IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 28

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Set Theory and Venn Diagrams, with the answer and a step-by-step solution.

Set Theory and Venn DiagramsModern MathematicsMultiple choiceMedium
In a group of 60 students, 35 study Mathematics, 30 study Physics, and 25 study Chemistry. Also, 15 study Mathematics and Physics, 12 study Physics and Chemistry, and 10 study Mathematics and Chemistry. These pairwise counts include the 5 students who study all three subjects. How many students study exactly one subject?
  1. A
    26
  2. B
    36
  3. C
    41
  4. D
    31
Pick an option, then check.
Answer & solution

Answer: Option D

For each subject, subtract the two overlapping pairs and add back the triple, which was removed twice.

Only Mathematics = 35 − 15 − 10 + 5 = 15.

Only Physics = 30 − 15 − 12 + 5 = 8.

Only Chemistry = 25 − 12 − 10 + 5 = 8.

Students studying exactly one subject = 15 + 8 + 8 = 31.

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