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.
There are four racks numbered 1, 2, 3, 4 and four books numbered 1, 2, 3, 4. If an even rack has to contain an odd numbered book and an odd rack contains an even numbered book, then what is the position of book 4?

• A. Second book has been put in third rack
• B. If any one of the statements alone is sufficient to answer the question
• C. If both statements individually are sufficient to answer the question
• D. If both statements together are required to answer the question

Hint:

For data sufficiency, test each statement independently first. If either gives a unique solution, option (A) is correct.

Answer 1

The Correct Option is A

We are told that: - Even rack ⇒ odd book, and - Odd rack ⇒ even book Using Statement (I) alone: Book 2 (even) is in rack 3 (odd) — consistent with the rule. Now the possible placements for the other books are narrowed significantly.
With Book 2 in rack 3, and applying the constraints to odd/even pairs, there is only one valid place for Book 4 (even) — it must go to another odd rack, either rack 1 or rack 3. But rack 3 is already occupied. So Book 4 must be in rack 1. Thus, statement (I) alone is sufficient.
Statement (II) alone: Book 3 (odd) is in rack 2 (even) — also consistent. Applying the same reasoning, we can also deduce that Book 4 goes to a unique rack (using parity constraint). Hence, (II) alone is also sufficient. Therefore, each statement alone is sufficient. \[ {\text{(A)}} \]