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

Since we want the worst possible rank for Vicky, it helps to think of this as “using up” the best available slots on students who don't need to beat her, and see how far down Vicky can be squeezed.

1. Raman-highest fixes Raman at rank 1 and Tony at rank 7, leaving ranks 2 through 6 open.
2. Sunil and Deepak have no ordering rule tying them to Vicky, Priya or Ankit, so they can freely take the two best open ranks, 2 and 3, to push everyone else down as far as possible.
3. That leaves ranks 4, 5, 6 for Vicky, Priya, Ankit, and the rule Vicky better than Priya better than Ankit forces this exact order: Vicky-4, Priya-5, Ankit-6.
4. Trying to push Vicky down even further, say to rank 5, would need both Priya and Ankit to fit into rank 6 alone, which is impossible for two people.

So rank 4 is the worst Vicky can ever be pushed to under these rules.

The correct answer is option C, fourth.