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# There are n new students in a class. Among any three of them, there ex

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Math Expert
Joined: 02 Sep 2009
Posts: 64144
There are n new students in a class. Among any three of them, there ex  [#permalink]

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01 Nov 2019, 04:42
46
00:00

Difficulty:

95% (hard)

Question Stats:

30% (01:56) correct 70% (02:09) wrong based on 169 sessions

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There are n new students in a class. Among any three of them, there exist two who know each other and among any four of them, there exist two who do not know each other. Find the greatest possible value of n.

A. 7
B. 8
C. 9
D. 10
E. 11

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Intern
Joined: 26 Nov 2019
Posts: 47
Location: India
GMAT 1: 650 Q48 V31
Re: There are n new students in a class. Among any three of them, there ex  [#permalink]

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18 Apr 2020, 18:58
1
jcgomezlv Kinshook

To my understanding
1) Among any three people two know each other
Lets assume three people as X X Y - 2 people know each other
2) Among any four people two do not know each other
Assuming four people as X X Y Z - Author mentions about Y and Z

Now combining together the rule to get maximum number of students
We might mistakenly assume
XXY & XXYZ and come up with 7

But here's the catch the class can have
2 sets of XXYZ because from this set if you pick 3 you can arrive at XXY (XXY is a subset of XXYZ)
so the maximum possible class value is XXYY XXYY -> 8 members
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Re: There are n new students in a class. Among any three of them, there ex  [#permalink]

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01 Nov 2019, 07:13
1
giving a try

Among any three of them, there exist two who know each other ; 3 and among any four of them, there exist two who do not know each other
3c2*2+2c1 = 8
IMO B

Bunuel wrote:
There are n new students in a class. Among any three of them, there exist two who know each other and among any four of them, there exist two who do not know each other. Find the greatest possible value of n.

A. 7
B. 8
C. 9
D. 10
E. 11

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CEO
Joined: 03 Jun 2019
Posts: 2891
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: There are n new students in a class. Among any three of them, there ex  [#permalink]

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28 Mar 2020, 02:00
Hi Archit3110

Please provide similar questions and methods to solve them.

Archit3110 wrote:
giving a try

Among any three of them, there exist two who know each other ; 3 and among any four of them, there exist two who do not know each other
3c2*2+2c1 = 8
IMO B

Bunuel wrote:
There are n new students in a class. Among any three of them, there exist two who know each other and among any four of them, there exist two who do not know each other. Find the greatest possible value of n.

A. 7
B. 8
C. 9
D. 10
E. 11

Are You Up For the Challenge: 700 Level Questions

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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
CEO
Joined: 03 Jun 2019
Posts: 2891
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: There are n new students in a class. Among any three of them, there ex  [#permalink]

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28 Mar 2020, 02:08
Bunuel wrote:
There are n new students in a class. Among any three of them, there exist two who know each other and among any four of them, there exist two who do not know each other. Find the greatest possible value of n.

A. 7
B. 8
C. 9
D. 10
E. 11

Are You Up For the Challenge: 700 Level Questions

Hi Bunuel
Please provide OE for the above question.
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Intern
Joined: 15 Dec 2018
Posts: 11
Re: There are n new students in a class. Among any three of them, there ex  [#permalink]

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10 Apr 2020, 03:50
Can someone help with an answer?

For me is really difficult, I do not know were to start

Juan

[quote="Bunuel"]There are n new students in a class. Among any three of them, there exist two who know each other and among any four of them, there exist two who do not know each other. Find the greatest possible value of n.

A. 7
B. 8
C. 9
D. 10
E. 11
Re: There are n new students in a class. Among any three of them, there ex   [#permalink] 10 Apr 2020, 03:50