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.

92. Each of the following must be false EXCEPT:

• A. Rudra is the only film buff to see the Guru Dutt film.
• B. Rudra is the only film buff to see the Satyajit Ray film.
• C. Yogi is the only film buff to see the Ritwik Ghatak film.
• D. Exactly two film buffs see the Ritwik Ghatak film.

Hint:

Check the group-size limits (Guru Dutt is 1 or 2, Satyajit Ray is 2 or 4, Ritwik Ghatak is 4 or 1) before testing the individual claims; most of these options fail on size alone.

Answer 1

The Correct Option is A

Step 1: Recall the two possible group-size splits.
As before, the only counts that satisfy "Satyajit Ray count = 2 x Guru Dutt count" across 7 people are Guru Dutt 1 / Satyajit Ray 2 / Ritwik Ghatak 4, or Guru Dutt 2 / Satyajit Ray 4 / Ritwik Ghatak 1.

Step 2: Check the "exactly three see Satyajit Ray" and "exactly two see Ritwik Ghatak" claims against these counts.
One of the original five choices claims exactly three film buffs see Satyajit Ray. But Satyajit Ray can only ever be 2 or 4 people, never 3, so that claim is always false and was dropped in the fold.
Option 4 says exactly two film buffs see Ritwik Ghatak. Ritwik Ghatak can only ever be 4 or 1 people, never 2, so option 4 is always false too.

Step 3: Check option 2 and option 3.
Option 2 needs Rudra to be the ONLY Satyajit Ray viewer, meaning Satyajit Ray has exactly 1 person. But Satyajit Ray is always 2 or 4, never 1, and Lalatakshaya is always there too, so Rudra could never be the sole viewer anyway. Always false.
Option 3 needs Yogi to be the only Ritwik Ghatak viewer. But Vyomkesha and Yogi always see the same film, so if Yogi is in Ritwik Ghatak, Vyomkesha is there too, meaning Yogi can never be the sole viewer. Always false.

Step 4: Test option 1 for a real arrangement.
Option 1 needs Rudra to be the only Guru Dutt viewer, meaning Guru Dutt = 1 person = Rudra, which fits the first split (Guru Dutt 1, Satyajit Ray 2, Ritwik Ghatak 4). Since Gangadhar cannot be in Satyajit Ray and Guru Dutt is taken by Rudra alone, Gangadhar must be in Ritwik Ghatak. Vyomkesha and Yogi also go to Ritwik Ghatak, since Satyajit Ray is already full with Lalatakshaya plus one more. That leaves Indra and Maheshwar to split the last Satyajit Ray seat and the last Ritwik Ghatak seat between them, which satisfies "Indra and Maheshwar do not see the same film." For example: Rudra = Guru Dutt, Lalatakshaya and Indra = Satyajit Ray, Gangadhar, Maheshwar, Vyomkesha, Yogi = Ritwik Ghatak. Every rule holds, and Rudra is indeed the only Guru Dutt viewer. So option 1 can be true.

Final Answer:
Options 2, 3, and 4 (and the dropped "exactly three see Satyajit Ray" claim) are always false, so option 1 is the one that is not necessarily false, and it is the answer.