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O is D.

Since there are at least 3 people in the room, D is inconsistent since those 3 people will all recognise each other, but we are told that at most 2 people recognise each other. Inconsistent.

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I hope the attachment allows everyone to visualize the problem.
Marked in Red is 2 people relationship
Marked in Blue is the 3 people relationship.

Rule out all those which are consistent with this diagram. The answer is the one which is left out.
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three people.png
three people.png [ 48.71 KiB | Viewed 15058 times ]

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Given:
1. Minimum 3 people in the room (ie >=3)
2. Maximum 2 people recognize each other
3. Minimum 1 person knows everyone in the room


(A) Four people are in the room. - Conditions 1, 2, 3 are satisfied - Incorrect
(B) No two people in the room recognize each other. - If there are 4 people in the room, then all the conditions are statisfied and there would be two people in the room who would not recognize each other - Incorrect
(C) At most one person in the room recognizes everybody else in the room. - Can be inferred from the passage. Plugging in few values would help conclude the same - Incorrect
(D) Anyone in the room who recognizes any other person in the room is also recognized by that person. - When there are 5 people in the room and only two people recognize each other. Additionally two persons know everyone in the room, the likelihood of such a scenario is very less - Correct
(E) Two people in the room recognize every one else in the room. - Can be the case when there are 4 people in the room and still satisfy all the conditions - Incorrect
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can anyone elaborate how to eliminate B . .i assumed a situation that A called x no of people so he recognises all. nobody else knows each other .this will fulfill all conditions in question and B is not possible. as all x might recognise A they just dont know the remaining x-1 people. . does my situation contradict anything in the question ?
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Let's imagine four people: Bob, Dave, Steve, and Joe. Bob recognizes Dave and Joe. Dave recognizes Joe and Joe recognizes Steve. However, this recognition is one way. Meaning just because someone recognizes you does not mean you will recognize them. Therefore, we can see that (D) does not have to be true. Therefore, the answer is (D).
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