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

Step 1: Work out what film Gangadhar and Vyomkesha share.
Gangadhar can only see Guru Dutt or Ritwik Ghatak, never Satyajit Ray. Vyomkesha (together with Yogi) can never be in Guru Dutt either, because that group is too small to hold two people in either valid split without breaking the Indra-Maheshwar rule, as shown in earlier questions. So Vyomkesha only ever sees Satyajit Ray or Ritwik Ghatak. If Vyomkesha and Gangadhar see the same film, the only film open to both of them is Ritwik Ghatak. So Gangadhar, Vyomkesha, and Yogi all see the Ritwik Ghatak film.

Step 2: Pin down the group sizes.
Three people (Gangadhar, Vyomkesha, Yogi) are already in Ritwik Ghatak, so Ritwik Ghatak has at least 3 seats. Only the split Guru Dutt 1 / Satyajit Ray 2 / Ritwik Ghatak 4 allows that (the other split has Ritwik Ghatak = 1). So we are in this split, and exactly 1 more person joins Ritwik Ghatak, making it 4. Lalatakshaya is fixed in Satyajit Ray, and Satyajit Ray needs exactly 1 more person to reach 2. Guru Dutt needs exactly 1 person.

Step 3: Place Indra, Maheshwar, and Rudra.
These three must fill the 1 remaining Guru Dutt seat, the 1 remaining Satyajit Ray seat, and the 1 remaining Ritwik Ghatak seat, one each. Since Gangadhar is in Ritwik Ghatak, Rudra cannot also be in Ritwik Ghatak (Gangadhar and Rudra must differ), so Rudra must take Guru Dutt or Satyajit Ray. This still leaves several valid arrangements, for example Indra = Satyajit Ray, Maheshwar = Ritwik Ghatak, Rudra = Guru Dutt, which satisfies every rule (Indra and Maheshwar differ, Gangadhar and Rudra differ, the 2-to-1 count holds). In this arrangement, Indra sees the Satyajit Ray film.

Step 4: Rule out the other options.
Gangadhar always ends up in Ritwik Ghatak under this condition, never Guru Dutt, so option 1 is always false. Rudra can never be in Ritwik Ghatak here (it would clash with Gangadhar), so option 3 is always false. Vyomkesha is always in Ritwik Ghatak, never Satyajit Ray, in this scenario, so option 4 is always false.

Final Answer:
Indra seeing the Satyajit Ray film is achievable, so option 2 is correct.