Question

Directions: Each group of questions in this section is based on a set of conditions. In answering some of the questions, it may help to draw a rough diagram. Choose the response that most accurately and completely answers each question.

Questions 91 to 96: Seven film buffs, Gangadhar, Indra, Lalatakshaya, Maheshwar, Rudra, Vyomkesha, and Yogi, attend a showing of classic films. Three films are shown, one each directed by Guru Dutt, Satyajit Ray, and Ritwik Ghatak. Each film buff sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions apply:

• Exactly twice as many of the film buffs see the Satyajit Ray film as see the Guru Dutt film.
• Gangadhar and Rudra do not see the same film as each other.
• Indra and Maheshwar do not see the same film as each other.
• Vyomkesha and Yogi see the same film as each other.
• Lalatakshaya sees the Satyajit Ray film.
• Gangadhar sees either the Guru Dutt film or the Ritwik Ghatak film.

95. If Vyomkesha and Gangadhar see the same film, then which one of the following could be true?

• A. Gangadhar sees the Guru Dutt film.
• B. Indra sees the Satyajit Ray film.
• C. Rudra sees the Ritwik Ghatak film.
• D. Vyomkesha sees the Satyajit Ray film.

Hint:

Gangadhar and Vyomkesha can only share Ritwik Ghatak, since Vyomkesha is never allowed in Guru Dutt; work out the group sizes from there.

Answer 1

The Correct Option is B

Start from what "Vyomkesha and Gangadhar see the same film" forces. Gangadhar's choices are limited to Guru Dutt or Ritwik Ghatak. Vyomkesha (tied to Yogi) can never sit in Guru Dutt, because that group never has room for two people without breaking the Indra-Maheshwar rule. So the only film Gangadhar and Vyomkesha can share is Ritwik Ghatak, which means Yogi is there too, giving Ritwik Ghatak at least 3 people. That only matches the split Guru Dutt 1, Satyajit Ray 2, Ritwik Ghatak 4, with exactly one more person filling out Ritwik Ghatak, and Indra, Maheshwar, Rudra dividing up the last Guru Dutt seat, the last Satyajit Ray seat, and that last Ritwik Ghatak seat.

1. Option 1 (Gangadhar sees Guru Dutt): we just showed Gangadhar is locked into Ritwik Ghatak whenever he matches Vyomkesha's film. He is never in Guru Dutt here, so this is always false.
2. Option 2 (Indra sees Satyajit Ray): try Indra = Satyajit Ray, Maheshwar = Ritwik Ghatak, Rudra = Guru Dutt. Check the rules: Gangadhar (Ritwik Ghatak) differs from Rudra (Guru Dutt), Indra (Satyajit Ray) differs from Maheshwar (Ritwik Ghatak), Vyomkesha matches Yogi, Lalatakshaya is in Satyajit Ray, and the count is 1 Guru Dutt to 2 Satyajit Ray. Everything checks out, so this can be true.
3. Option 3 (Rudra sees Ritwik Ghatak): Gangadhar already occupies Ritwik Ghatak in this scenario, and Gangadhar and Rudra can never share a film, so Rudra is never in Ritwik Ghatak here. Always false.
4. Option 4 (Vyomkesha sees Satyajit Ray): we already fixed Vyomkesha in Ritwik Ghatak for this whole scenario, since that is the only way Vyomkesha can match Gangadhar's film. So Vyomkesha is never in Satyajit Ray here. Always false.

Only option 2 can actually happen.

Let's summarize:

• Vyomkesha and Gangadhar matching films forces both of them, plus Yogi, into Ritwik Ghatak.
• That pins the group sizes to Guru Dutt 1, Satyajit Ray 2, Ritwik Ghatak 4, leaving Indra, Maheshwar, and Rudra to split the 3 leftover seats.

Indra seeing the Satyajit Ray film fits one of those valid splits, so option 2 is the answer.