In a meeting of 3 representatives from each of 6 different companies, each person shook hands with every person not from

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Sat May 15, 2021 8:02 am

GMAT Prep

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

OA B

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