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There are at least three people in the room. At most two [#permalink]
11 Mar 2010, 22:42

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Difficulty:

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Question Stats:

37% (02:54) correct
63% (01:47) wrong based on 105 sessions

There are at least three people in the room. At most two people in the room recognize each other. At least one person in the room recognizes everybody else in the room. Which one of the following is NOT consistent with the above? (A) Four people are in the room. (B) No two people in the room recognize each other. (C) At most one person in the room recognizes everybody else in the room. (D) Anyone in the room who recognizes any other person in the room is also recognized by that person. (E) Two people in the room recognize every one else in the room.

a recognizes b and c. (this is in line with the 3rd statement in the question.)

Choice D says that if a recognizes b and c then both b and c should in turn recognize a. But this contradicts the second statement that at most two people recognize each other.

Hence D is not consistent with the information given. _________________

There are at least three people in the room. At most two people in the room recognize each other. At least one person in the room recognizes everybody else in the room. Which one of the following is NOT consistent with the above? (A) Four people are in the room. (B) No two people in the room recognize each other. (C) At most one person in the room recognizes everybody else in the room. (D) Anyone in the room who recognizes any other person in the room is also recognized by that person. (E) Two people in the room recognize every one else in the room. OA

A: It is possible, question stem says atleast three people in room. B: Could be possible in case there are more than 3 people. C: True, given in question stem. D: False there is a person who soes not recognizes everybody E: True given in question stem.

at least one person recognizes everyone else in the room, and in D, if this one person has to be recognized by everyone else also, that indirectly suggests, according to the fact that everybody recognizes him, at least 3 people(which is provided) recognize each other, that is inconsistent with the other premise that at most only 2 could have recognized each other.

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Re: There are at least three people in the room. At most two [#permalink]
05 Aug 2012, 21:30

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

Re: There are at least three people in the room. At most two [#permalink]
11 Aug 2012, 05:44

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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Re: There are at least three people in the room. At most two [#permalink]
11 Aug 2012, 06:30

Expert's post

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). _________________