Question

T School of Management is a management institute involved in teaching, training and research. Currently it has 37 faculty members. They are involved in three jobs: teaching, training and research. Each faculty member working with IT School of Management has to be involved in at least one of the three jobs mentioned above: • A maximum number of faculty members are involved in training. Among them, a number of faculty members are having additional involvement in the research. • The number of faculty members in research alone is double the number of faculty members involved in all the three jobs. • 17 faculty members are involved in teaching. The number of faculty members involved in teaching alone is less than the number of faculty members involved in research alone. • The faculty members involved in the teaching are also involved in at least one more job.
Based on the information given above, the minimum number of faculty members involved in both training and teaching, but not in research is:

• A. 1
• B. 3
• C. 4
• D. 5
  % Correct answer \textbf{Correct answer:} (A) 1

Hint:

Use minimum logic by maximizing common intersections in Venn regions.

Answer 1

The Correct Option is A

Using Venn diagram or set logic: - Total = 37 members
- Teaching = 17, Training = 20, Research = 19
- Teaching overlaps with training and research, but no one in teaching alone.
We are to find the minimum in (Teaching ∩ Training) excluding Research. To minimize this count, we maximize overlaps in all three and other pairs. After exhausting distributions, the minimum value that satisfies the set equation gives: \[ {1} \]