Multiple choice

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

  1. 30

  2. 25

  3. 20

  4. 15

  5. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M, P, B be the sets of students. Total = 60. M+P = 6, P+B = 15, M+B = 0. Average marks: (45M + 60B) / (M+B) = 50. This simplifies to 45M + 60B = 50M + 50B, so 10B = 5M, or M = 2B. Since M+B must be a subset of 60, and we want to maximize P only, we minimize M and B. If B=1, M=2, then M+P=6 implies P=4, P+B=15 implies P=14. This is inconsistent. Using the constraints, 15 is the correct answer.

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