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

This puzzle is easiest to manage by first locking down every rank that is forced, and only then checking each option against what is left open.

1. Sunil at sixth rules out the “Sunil highest” branch, so Raman must be first and Tony must be seventh. These two ranks are now fixed and cannot change.
2. Ankit is fifth and Sunil is sixth, both given directly.
3. That leaves ranks 2, 3 and 4 for Vicky, Priya and Deepak, with the fixed requirement that Vicky ranks better than Priya (since Vicky always outscores Priya).
4. Vicky first or fourth: rank 1 belongs to Raman, and Vicky can never be pushed to fourth because Priya would then have nowhere worse to sit within the remaining slots; impossible.
5. Raman second or third: Raman's rank is locked at 1 in this branch; impossible.
6. Tony fourth or fifth: Tony's rank is locked at 7 in this branch; impossible.
7. Deepak third or fourth: with Vicky and Priya taking any two of {2, 3, 4} in the right order, Deepak simply takes whichever slot is left, and that can genuinely be 3 or 4 depending on the arrangement; possible.

Only the option about Deepak survives.

So the correct answer is option D.