Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least. Whenever F scores the highest, B scores the least. In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A. If B scores the least, the rank of C will be

Here's a brief explanation:

1. Given Condition: B scores the least (B=6th).

2. Deduction from Rule 3: "Whenever F scores the highest, B scores the least." Since B scores the least, F must score the highest (F=1st).

3. Current Ranks: F=1st, B=6th.

4. Remaining Students & Ranks: A, C, D, E must occupy ranks 2, 3, 4, 5.

5. Inequalities: We have C > A and D > A.

6. Interpreting "Close Competitors": The phrase "D scores higher than A, but they are close competitors" implies that D is immediately above A in rank (D's rank = A's rank - 1).

7. Possible Ranks for A:

   • A cannot be 2nd or 3rd, because D must be immediately above A, and F is already 1st.

   • Therefore, A can only be 4th or 5th.

   • Case 1: If A is 4th.

     • Then D must be 3rd (D=A-1).
     • Ranks so far: F=1, D=3, A=4, B=6.
     • Remaining students (C, E) must take ranks 2 and 5.
     • Since C > A (C > 4th), C must be 2nd. E is 5th.
     • Arrangement: F=1, C=2, D=3, A=4, E=5, B=6. Here, C is 2nd.

   • Case 2: If A is 5th.

     • Then D must be 4th (D=A-1).
     • Ranks so far: F=1, D=4, A=5, B=6.
     • Remaining students (C, E) must take ranks 2 and 3.
     • Since C > A (C > 5th), C must be either 2nd or 3rd. E takes the other rank.
     • Arrangement 1: F=1, C=2, E=3, D=4, A=5, B=6. Here, C is 2nd.
     • Arrangement 2: F=1, E=2, C=3, D=4, A=5, B=6. Here, C is 3rd.

8. Conclusion: Combining both cases, the rank of C can be 2nd or 3rd.

The final answer is D) 2nd or 3rd.