Question

Instructions: Seven students, Priya, Ankit, Raman, Sunil, Tony, Deepak and Vicky, take a series of tests. No two students get similar marks. Vicky always scores more than Priya. Priya always scores more than Ankit. Each time, either Raman scores the highest and Tony gets the least, or alternatively Sunil scores the highest and Deepak or Ankit scores the least.

If Sunil is ranked sixth and Ankit is ranked fifth, which of the following can be true?

• A. Vicky is ranked first or fourth
• B. Raman is ranked second or third
• C. Tony is ranked fourth or fifth
• D. Deepak is ranked third or fourth

Hint:

Sunil at sixth forces Raman to first and Tony to seventh; only Deepak’s rank among {2,3,4} is left flexible.

Answer 1

The Correct Option is D

Step 1: Fix the scenario.
Since Sunil is ranked sixth, he is not the highest scorer, so the “Sunil highest” branch cannot apply here. That forces the other branch: Raman is first (highest) and Tony is seventh (least).

Step 2: Place the remaining students.
Ankit is fifth (given) and Sunil is sixth (given). Since Vicky scores more than Priya, who scores more than Ankit, both Vicky and Priya must rank better than fifth, so they must occupy two of the ranks 2, 3 and 4 (rank 1 is Raman's), with Vicky ranked better than Priya. Deepak takes whichever of ranks 2, 3, 4 is left over.

Step 3: Check option A.
Vicky cannot be ranked first, since Raman holds that rank, and in every valid arrangement Priya must rank worse than Vicky within {2, 3, 4}, which never allows Vicky to be pushed down to fourth (there would be no room left for Priya to be worse than her). So option A is never possible.

Step 4: Check option B.
Raman is fixed at rank 1 in this scenario, so he can never be second or third. Option B is impossible.

Step 5: Check option C.
Tony is fixed at rank 7 in this scenario, so he can never be fourth or fifth. Option C is impossible.

Step 6: Check option D.
Deepak can occupy rank 2, 3 or 4 depending on how Vicky and Priya are arranged in the other two slots (for example Raman-1, Deepak-3, Vicky-2, Priya-4 works, and so does a version with Deepak-4). So Deepak being ranked third or fourth is genuinely possible.

Step 7: Final Answer.
Option D is the one that can be true.