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.
After some time, the faculty members who were involved in all the three tasks were asked to withdraw from one task. As a result, one of the faculty members each opted out of teaching and research, while remaining ones involved in all the three tasks opted out of training. Which one of the following statements, then necessarily follows:

• A. The least number of faculty members is now involved in teaching.
• B. More faculty members are now associated with training as compared to research.
• C. More faculty members are now involved in teaching as compared to research.
• D. None of the above
  % Correct answer \textbf{Correct answer:} (D) None of the above

Hint:

If exact quantities can't be derived due to incomplete overlap data, prefer conservative conclusions like "None of the above."

Answer 1

The Correct Option is D

The changes in task assignments involve complex overlaps and partial withdrawals from tasks. Given the information, the final relative quantities across teaching, training, and research are not precisely quantifiable. Hence, we cannot conclusively determine whether any one of the statements (A), (B), or (C) is necessarily true. Therefore, the correct answer is: \[ {\text{(D) None of the above}} \]