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double kiss

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by GmatKiss » Thu Sep 01, 2011 11:16 am
Six three-female-representative delegations attend a conference. The representatives give a double kiss on a check when they are introduced to one another. How many kisses on a check are possible if each delegate gives a double kiss on a check only once with every other attendant except with those of her delegation?

(A) 766
(B) 270
(C) 180
(D) 144
(E) 72

Please help to break this one!
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by akhilsuhag » Thu Sep 01, 2011 11:23 am
i really think thr is smthn wrong with the question!!

Sorry i misread the question.. it is clear now!!
Last edited by akhilsuhag on Thu Sep 01, 2011 11:37 am, edited 1 time in total.
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by thestartupguy » Thu Sep 01, 2011 11:35 am
IMO: B

(a)Let's say that Group 1 give kisses to Groups 2,3,4,5,6
Group 2 to Groups 3, 4, 5, 6. I have ignored Group 2 to 1 as it is same as Group 1 to 2

So,
1->2,3,4,5,6
2->3,4,5,6
3->4,5,6
4->5,6
5->6

(b) There are 15 groups. Each group consists three members. So when one group members kisses another group members. There are 9 kisses.

c) Answer = 15 (no. of groups) X 9 (kisses between two groups) X 2 (double kiss) = 270.

I have one doubt, If one person is double kissing another person, then there are 4 kisses exchanged at one time. This doubles my answer, 270 X 2 = 540.

Please tell me if my understanding of double kiss is wrong. Also, can you guys think of a better method than this?
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by GMATGuruNY » Thu Sep 01, 2011 11:40 am
GmatKiss wrote:Six three-female-representative delegations attend a conference. The representatives give a double kiss on a cheek when they are introduced to one another. How many kisses on a cheek are possible if each delegate gives a double kiss on a cheek only once with every other attendant except with those of her delegation?

(A) 766
(B) 270
(C) 180
(D) 144
(E) 72

Please help to break this one!
The total number of pairs that can be formed from 18 people = 18C2 = 153.
The total number of pairs that can be formed from each delegation of 3 and thus cannot kiss = 3C2 = 3.
Since there are 6 delegations, the total number of pairs that cannot kiss = 6*3 = 18.
Thus, the total number of pairs that kiss = 153-18 = 135.
Since each pair kisses twice, the total number of kisses = 2*135 = 270.

The correct answer is B.
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by saketk » Fri Sep 02, 2011 1:14 am
GmatKiss wrote:Six three-female-representative delegations attend a conference. The representatives give a double kiss on a check when they are introduced to one another. How many kisses on a check are possible if each delegate gives a double kiss on a check only once with every other attendant except with those of her delegation?

(A) 766
(B) 270
(C) 180
(D) 144
(E) 72

Please help to break this one!
Total member = 18
total kisses = 2* 18C2 = 306
Subtract the cases when the delegates kissed within the group
Say (A-B-C) = 3 cases. Total kisses in each group= 3*2=6
Total = 6*6 = 36 kisses within the groups.

The answer = 306-36 = 270 (Too many kisses:) )

option B
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