There are at least three people in the room. At most two : GMAT Critical Reasoning (CR)
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# There are at least three people in the room. At most two

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There are at least three people in the room. At most two [#permalink]

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11 Mar 2010, 22:42
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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
[Reveal] Spoiler:
d

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13 Mar 2010, 02:34

Let a, b, c be 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.
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13 Mar 2010, 07:23
vaivish1723 wrote:
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
[Reveal] Spoiler:
d

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.

Hence D
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13 Mar 2010, 11:26
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+1 for D
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09 Jul 2010, 00:55
D
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09 Jul 2010, 01:43
My choice is D.
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03 Aug 2010, 23:34
D .it is .....
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06 Aug 2010, 07:24
+1 for D
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06 Aug 2010, 16:59
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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11 Sep 2010, 07:27
D it is
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Re: There are at least three people in the room. At most two [#permalink]

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05 Aug 2012, 05:22
ha ha i didnt even get the idea behind the answers! anyways guys thanks for posting OA and explanation. I feel enlightened
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Re: There are at least three people in the room. At most two [#permalink]

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05 Aug 2012, 05:35
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.
Attachments

three people.png [ 48.71 KiB | Viewed 1781 times ]

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Re: There are at least three people in the room. At most two [#permalink]

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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
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Re: There are at least three people in the room. At most two [#permalink]

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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]

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

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11 Aug 2012, 08:50
@chrislele . . sir , doesn't the question ask which of following cannot be true rather than which one does not have to be true ??

and @ mourinhogmat1 . the diagram does not follow last condition. that one person knows all in the room.
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Re: There are at least three people in the room. At most two [#permalink]

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14 Jun 2015, 10:42
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Re: There are at least three people in the room. At most two [#permalink]

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16 Jun 2015, 11:36
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.

Answer B means that there are no two persons in the room who do not know each other but the stimuli is saying that there are maximum two people in the room who recognizes each other. Are not they conflicting each other? Then how to eliminate B
Re: There are at least three people in the room. At most two   [#permalink] 16 Jun 2015, 11:36
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