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.

91. Which one of the following could be an accurate matching of film buffs to films?

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

Hint:

Work out the two valid film-count splits first (1-2-4 or 2-4-1), then use the Vyomkesha-Yogi rule to see which film they must share.

Answer 1

The Correct Option is D

Step 1: Set up what the film counts can be.
Seven film buffs split across three films: Guru Dutt (GD), Satyajit Ray (SR), and Ritwik Ghatak (RG). The rule says SR = 2 x GD. Since Lalatakshaya is fixed in SR, GD cannot be 0. Testing GD = 1, 2, 3 against GD + SR + RG = 7 shows only two counts work: GD = 1, SR = 2, RG = 4, or GD = 2, SR = 4, RG = 1 (GD = 3 would need SR = 6, leaving a negative RG, which is impossible).

Step 2: Use the Vyomkesha-Yogi rule to narrow the split further.
Vyomkesha and Yogi always sit in the same film group, so that group needs at least 2 seats. In the GD = 1, SR = 2, RG = 4 case, SR already holds Lalatakshaya and has only 1 seat left, so Vyomkesha and Yogi cannot both fit there, and GD has only 1 seat too, so they must both be in Ritwik Ghatak. In the GD = 2, SR = 4, RG = 1 case, RG has only 1 seat, so Vyomkesha and Yogi cannot sit there either; if they both took the 2 Guru Dutt seats, Gangadhar (who can only be GD or RG) would be pushed into the single RG seat, and Indra, Maheshwar, Rudra would all have to fill the remaining 3 Satyajit Ray seats, forcing Indra and Maheshwar into the same film, which breaks their rule. So in this case too, Vyomkesha and Yogi must sit in Satyajit Ray.

Step 3: Test each option against these two valid families.
Option 1 puts Gangadhar in the Satyajit Ray film, but Gangadhar can only see Guru Dutt or Ritwik Ghatak, so this fails right away.
Option 2 needs Vyomkesha in Guru Dutt, which Step 2 already ruled out (Vyomkesha only ever sits in Ritwik Ghatak or Satyajit Ray), so it fails.
Option 3 also needs Vyomkesha in Guru Dutt, so it fails for the same reason.
Option 4 places Maheshwar, Rudra, and Vyomkesha (so also Yogi) all in Ritwik Ghatak. Take the GD = 1 family: let Gangadhar take the single Guru Dutt seat, Indra join Lalatakshaya in Satyajit Ray, and Maheshwar, Rudra, Vyomkesha, Yogi fill all 4 Ritwik Ghatak seats. Check every rule: SR (2) is twice GD (1); Gangadhar and Rudra differ (GD vs RG); Indra and Maheshwar differ (SR vs RG); Vyomkesha equals Yogi (both RG); Lalatakshaya is SR; Gangadhar is GD. Every condition holds, so this matching is possible.

Final Answer:
Option 4 is the only matching that can actually happen.