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.

94. If exactly one film buff sees the Ritwik Ghatak film, then which one of the following must be true?

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

Hint:

An Ritwik Ghatak count of exactly 1 only fits one group-size split; work out where Vyomkesha and Yogi end up in that split.

Answer 1

The Correct Option is A

Step 1: Figure out which group-size split gives exactly one Ritwik Ghatak viewer.
The two valid splits are Guru Dutt 1 / Satyajit Ray 2 / Ritwik Ghatak 4, or Guru Dutt 2 / Satyajit Ray 4 / Ritwik Ghatak 1. Since we are told exactly one person sees Ritwik Ghatak, we are in the second split: Guru Dutt 2, Satyajit Ray 4, Ritwik Ghatak 1.

Step 2: Work out where Vyomkesha and Yogi must sit.
Ritwik Ghatak has only 1 seat, so Vyomkesha and Yogi (who always sit together) cannot both be there. Could they both be in Guru Dutt (2 seats)? If so, Gangadhar (who can only sit in Guru Dutt or Ritwik Ghatak) would have no room left in Guru Dutt and would have to take the lone Ritwik Ghatak seat. That leaves Indra, Maheshwar, and Rudra to fill all 3 remaining Satyajit Ray seats, but then Indra and Maheshwar would both be in Satyajit Ray, breaking the rule that they must see different films. So Vyomkesha and Yogi cannot be in Guru Dutt either. The only group left with room for both of them is Satyajit Ray (4 seats), so Vyomkesha and Yogi must both see the Satyajit Ray film.

Step 3: Confirm this against the other statements.
Since Vyomkesha must be in Satyajit Ray in every valid seating under this condition, option 1 must be true. The other three statements are not forced: for example, Gangadhar = Guru Dutt, Indra = Guru Dutt, Rudra = Ritwik Ghatak, Maheshwar = Satyajit Ray is one valid seating, and Gangadhar = Ritwik Ghatak, Indra = Guru Dutt, Rudra = Guru Dutt, Maheshwar = Satyajit Ray is another, so options 2, 3, and 4 each fail to hold in at least one valid seating.

Final Answer:
Vyomkesha must see the Satyajit Ray film, so option 1 is correct.