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GRE · Question of the Day

GRE Question of the Day

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Thursday, September 17, 2026

In a group of 60 students, let set MM be the students who study Math and set PP be the students who study Physics. If ∣M∣=35|M|=35, ∣P∣=28|P|=28, and ∣M∩P∣=15|M\cap P|=15, how many students study neither Math nor Physics?

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Question of the Day

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In a group of 60 students, let set MM be the students who study Math and set PP be the students who study Physics. If ∣M∣=35|M|=35, ∣P∣=28|P|=28, and ∣M∩P∣=15|M\cap P|=15, how many students study neither Math nor Physics?

  1. 12 (correct answer)
  2. 3
  3. 10
  4. 32
  5. 18

Explanation: This question tests set theory reasoning using Venn diagrams for two overlapping sets. We model the students in Math (M) and Physics (P) with regions for only M, only P, and both. The intersection |M ∩ P| = 15 represents students studying both subjects. The number studying only Math is 35 - 15 = 20, and only Physics is 28 - 15 = 13. The total studying at least one subject is 20 + 13 + 15 = 48, so those studying neither is 60 - 48 = 12. A common incorrect option arises from adding |M| and |P| without subtracting the intersection, leading to 35 + 28 = 63 and 60 - 63 = -3, which is impossible and highlights the error of double-counting the overlap.