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There are at least three people in the room. At most two people in the

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

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New post Updated on: 09 Oct 2018, 08:19
1
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (01:52) correct 60% (01:31) wrong based on 126 sessions

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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.

Originally posted by vaivish1723 on 25 Jan 2010, 10:09.
Last edited by Bunuel on 09 Oct 2018, 08:19, edited 1 time in total.
Renamed the topic and edited the question.
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Re: There are at least three people in the room. At most two people in the  [#permalink]

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New post 28 Jan 2010, 04:38
Rule#1: There are at least three people in the room. (Room has >=3people)
Rule#2: At most two people in the room recognize each other. (Max 2 people recognize each other)
Rule#3: At least one person in the room recognizes everybody else in the room. (>= 1 person recog. everyone else)

(A) Four people are in the room.
Consistent. This does not violate any rule above.
(B) No two people in the room recognize each other.
Consistent. Relates to the Rule #2. Rule says that at max. there can be 2 people who recognize each other and at the minimum there can be 0 people. Here 0 people recognize each other. Hence consistent.
(C) At most one person in the room recognizes everybody else in the room.
Consistent. Rule #3. Answer can be >= 1. Here it is 1.
(D) Anyone in the room who recognizes any other person in the room is also recognized by that person.
Not consistent. Violates Rule #2. Because of the number of people in the room is 3, then all the 3 recognize each other. And this is more than 2 people. Hence not consistent.
(E) Two people in the room recognize every one else in the room.
Consistent. Based on Rule #3. (>= 1 person)
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Re: There are at least three people in the room. At most two people in the  [#permalink]

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New post 29 Oct 2011, 22:43
Picked D in 89 seconds.

Strategy: Pick 3 or 4 as the total number of people in the room and then apply all 3 rules ( including the one in the answer choice under scrutiny). This will clearly show a disagreement in D.
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Re: There are at least three people in the room. At most two people in the  [#permalink]

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New post 22 Jun 2012, 09:01
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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Re: There are at least three people in the room. At most two  [#permalink]

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New post 05 Aug 2012, 06:35
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
three people.png [ 48.71 KiB | Viewed 2848 times ]

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

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New post 05 Aug 2012, 22:30
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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New post 11 Aug 2012, 06:44
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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New post 11 Aug 2012, 07:30
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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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Re: There are at least three people in the room. At most two people in the  [#permalink]

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New post 09 Oct 2018, 08:22
Hello from the GMAT Club VerbalBot!

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Re: There are at least three people in the room. At most two people in the &nbs [#permalink] 09 Oct 2018, 08:22
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