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 Raman gets the highest score, Vicky should be ranked not lower than:

• A. Second
• B. Third
• C. Fourth
• D. Fifth

Hint:

Give the best free ranks to Sunil and Deepak first; Vicky, Priya, Ankit then must fill the remaining three ranks in that fixed order.

Answer 1

The Correct Option is C

Step 1: Fix the scenario.
Raman scoring highest means Tony is last (seventh) in this branch, both fixed. The remaining ranks 2 to 6 go to Vicky, Priya, Ankit, Sunil and Deepak, with the requirement Vicky better than Priya better than Ankit (in that order of rank).

Step 2: Push Vicky as low as possible.
To make Vicky's rank as bad as possible, give the best remaining ranks to students with no ordering constraint relative to her, namely Sunil and Deepak, placing them at ranks 2 and 3. That leaves ranks 4, 5 and 6 for Vicky, Priya and Ankit, and since Vicky must beat Priya who must beat Ankit, the only order that fits is Vicky-4, Priya-5, Ankit-6.

Step 3: Check this is valid.
This gives the full order: Raman-1, Sunil-2, Deepak-3, Vicky-4, Priya-5, Ankit-6, Tony-7, which satisfies every condition in the problem.

Step 4: Check Vicky cannot go any lower.
If Vicky were pushed to rank 5, then Priya and Ankit would both need ranks worse than 5, but only rank 6 remains before Tony's fixed rank 7, which is not enough room for two people. So Vicky cannot be ranked fifth or worse.

Step 5: Final Answer.
The worst (lowest) Vicky can be ranked is fourth, so option C is correct.