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In a meeting of 3 representatives from each of 6 different c
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02 Sep 2020, 09:48
02 Sep 2020, 09:48
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Question Stats:
58% (01:41) correct
41% (01:03) wrong based on 34 sessions
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In a meeting of 3 representatives from each of 6 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?
A. 45
B. 135
C. 144
D. 270
E. 288
A. 45
B. 135
C. 144
D. 270
E. 288
Re: In a meeting of 3 representatives from each of 6 different c
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02 Sep 2020, 09:49
02 Sep 2020, 09:49
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
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Re: In a meeting of 3 representatives from each of 6 different c
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02 Sep 2020, 10:11
02 Sep 2020, 10:11
Carcass wrote:
In a meeting of 3 representatives from each of 6 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?
A. 45
B. 135
C. 144
D. 270
E. 288
A. 45
B. 135
C. 144
D. 270
E. 288
Let's focus on 1 person, call him Ted from company A.
Ted will shake hands with a total of 15 people (all 3 people who are in the other 5 companies).
Likewise, Ann from Company B will also shake hands with 15 people.
And so on....
In fact, all 18 people will shake hands with 15 others.
So, it SEEMS like the TOTAL number of handshakes = (18)(15)
HOWEVER, we need to keep in mind that we have counted each handshake TWICE.
That is, if Ted shakes hands with Ann, then we have counted that handshake once in Ted's 15 handshakes, AND once in Ann's 15 handshakes.
And so on...
To account for this DUPLICATION, we must divide (18)(15) by 2.
So, the TOTAL # of handshakes = (18)(15)/2 = 135 = B
Cheers,
Brent
