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by Brent@GMATPrepNow » Mon Apr 25, 2016 6:55 pm
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
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

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by MartyMurray » Mon Apr 25, 2016 7:01 pm
girishj wrote:At a meeting of 3 representatives from each of 6 different companies, each person shook hands once with every person not from his or her own company. If the representatives did not shake hands with people from their own companies, how many handshakes took place?

(A) 45

(B) 135

(C) 144

(D) 270

(E) 288
There are 3 representatives from each of 6 companies. So there are 3 x 6 = 18 representatives.

Each representative shook hands with everyone not from his or her company.

18 representatives each shook hands with 18 - 3 = 15 representatives.

Each handshake involves two people. So when one person shakes hands with another person, the other person also shakes hands with the first person.

So to eliminate duplicate handshakes you have to divide by 2.

(18 shook hands with 15)/2 = (18 x 15)/2 = 9 x 15 = 135

The correct answer is B.
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by GMATGuruNY » Mon Apr 25, 2016 7:04 pm
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
Total number of representatives = (number of representatives per company)(total number of companies) = 3*6 = 18.

Good handshakes = total possible handshakes - bad handshakes.

Total possible handshakes:
From the 18 representatives, the total number of pairs that could shake hands = 18C2 = (18*17)/(2*1) = 153.

Bad handshakes:
A bad handshake occurs when a pair of representatives from the same company shake hands.
From each group of 3 representatives from the same company, the total number of pairs that could shake hands = 3C2 = (3*2)/(2*1) = 3.
Since there are 6 companies -- and each company yields a total of 3 bad handshakes -- the total number of bad handshakes = 6*3 = 18.

Good handshakes:
(total possible handshakes) - (bad handshakes) = 153 - 18 = 135.

The correct answer is B.
Last edited by GMATGuruNY on Tue Apr 26, 2016 7:22 am, edited 1 time in total.
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by girishj » Tue Apr 26, 2016 7:14 am
Thanks to all you guys. Deeply appreciated. I have posted few other questions in SC, CR and RC for which I haven't received any responses at all. May I request you'll to provide replies for those as well. My GMAT is just around the corner. Thanks in advance
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by Jeff@TargetTestPrep » Thu Dec 14, 2017 4:37 pm
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
We are given that there are 3 representatives from 6 different companies. So, there are a total of 18 representatives.

If every representative were to shake hands with all other representatives (meaning all 18 reps would shake hands), this would happen in the following number of ways:

18C2 = (18 x 17)/2! = 9 x 17 = 153 ways

However, since each person shook hands with every person not from his or her own company, we can subtract out the number of times those handshakes occurred.

Since each company has 3 reps, the number ways those three reps can shake hand is 3C2 = (3 x 2)/2! = 3 ways, and since there are 6 companies, this would occur 6 x 3 = 18 times.

Thus, the number of ways for the reps to shake hands with every person not from his or her own company is 153 - 18 = 135 ways.

Answer: B

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by Brent@GMATPrepNow » Thu Dec 14, 2017 4:55 pm
Six companies attend a workshop - each is represented by three employees. All employees, except those from the same companies, shake hands to greet. How many hand-shakes were exchanged?
a) 102
b) 123
c) 135
d) 193
e) 288
There are 18 attendees altogether.

If you ask any attendee, "How many people did you shake hands with?", he/she will say 15, because that person will shake hands with the 15 people that are not in his/her company.

So, the TOTAL number of handshakes = (18)(15) = 270

But wait, we have counted every handshake TWICE. Person A counted his/her handshake with person G, and person G counted his/her handshake with person person A.

To account for this duplication, we must divide 270 by 2 to get 135.

Cheers,
Brent
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