January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 22 Aug 2014
Posts: 15
Location: United States
Concentration: Human Resources, General Management
GPA: 3.97
WE: Information Technology (Insurance)

In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
Updated on: 10 Apr 2016, 09:12
Question Stats:
63% (01:05) correct 37% (01:03) wrong based on 744 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by surupab on 10 Apr 2016, 07:22.
Last edited by Bunuel on 10 Apr 2016, 09:12, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Aug 2009
Posts: 7199

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
10 Apr 2016, 08:29
surupab 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? A45 B135 C144 D270 E288 Another way Lets count the total number of handshakes = 18C2= 153..
Out of these within company handshakes = 3C2=3 and no of companies=6 so total handshakes within company = 6*3=18
Handshakes with given restrictions = 15318= 135B
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor




Intern
Joined: 21 Jan 2016
Posts: 22
Location: India
GPA: 2.4
WE: Manufacturing and Production (Manufacturing)

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
10 Apr 2016, 08:02
I don't know any shortcut to this question but here's what i counted: There are total 18 people from 6 companies,3 from each.Now each of them starts shaking hands one by one with other companies representative. If the companies are A,B,C,D,E,F. Each member from company A gets to shake hands with 15 people(Total 18 minus member from his company and himself). Then each member from company B shakes hands with 12 people because they already shook hands with company A members. Similarly company C member shakes hand with 9 members and so on. so we have (15*3)+(12*3)+(9*3)+(6*3)+(3*3) = 135
_________________
GREEN ORANGE YELLOW RED




Math Expert
Joined: 02 Aug 2009
Posts: 7199

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
10 Apr 2016, 08:26
surupab 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? A45 B135 C144 D270 E288 Hi prashant212, a short cut would be... choose two companies out of 6 = 6C2.. the hand shakes with in these two companies = 3*3=9.. Total handshakes = 6C2 * 9 = 15 * 9 =135B
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



CEO
Joined: 11 Sep 2015
Posts: 3325
Location: Canada

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
10 Apr 2016, 09:34
surupab 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 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
_________________
Test confidently with gmatprepnow.com



SVP
Joined: 06 Nov 2014
Posts: 1877

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
11 Jul 2016, 20:22
surupab 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 Total employees = 6*3 = 18 Total number of handshakes = 18C2 = 153 Undesired handshakes = hand shakes between employers of same company = 3C2 = 3 Total undesired handshakes = 6*3 = 18 Total handshakes exchanged = 153  18 = 135 Correct Option: B



Intern
Joined: 07 Jun 2016
Posts: 37
GPA: 3.8
WE: Supply Chain Management (Manufacturing)

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
12 Oct 2016, 18:05
chetan2u wrote: surupab 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? A45 B135 C144 D270 E288 Hi prashant212, a short cut would be... choose two companies out of 6 = 6C2.. the hand shakes with in these two companies = 3*3=9.. Total handshakes = 6C2 * 9 = 15 * 9 =135B Excellent explanation and I only got this right going the long route....I am struggling with combinations more than I thought I would...I get a few steps correct but then leave a crucial one out. I will continue to practice using your laid out approach



Director
Joined: 17 Dec 2012
Posts: 625
Location: India

In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
21 May 2017, 18:51
surupab 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 1. It is a combination problem 2. Is there a constraint? The constraint is a person does not shake hand with another person of his own company. 3. Assume the opposite of the constraint. The person shakes hand with another person of the same company 4. Total number of combinations is 18C2= 153 5. Opposite of the constraint is 3 handshakes within same company men * total of 6 companies=18 6. Number of handshakes with constraints is (4)(5)= 135
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
23 May 2017, 16:21
surupab 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 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
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 30 Mar 2016
Posts: 40

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
18 Jan 2018, 01:55
Hi all,
Each company has 3 representatives and there are 6 companies. So there are 18 people in the meeting.
One handshake needs 2 people participating since people are NOT shaking their own hands.
So the question would be: in how many ways we can choose 2 people out of 18 people.
Let say there are 2 slots: __A __B
There are 18 possibilities for A.
There are 15 possibilities for B. Why?
+The person picked for A can NOT be shaking his/her own hand. So there are 18  1 = 17 people left to choose for B
+The person picked for A also can NOT be shaking his/her colleagues' hands. So there are 17  2 = 15 people left to choose for B.
So there are 18 x 15 = 270 handshakes, assuming that AB is DIFFERENT from BA. This means that A shaking B's hand is DIFFERENT from B shaking A's hands.
But, logically they are all the SAME  A shakes B's hand = B shakes A's hand.
So of 270 handshakes, there are 2! handshakes being OVERCOUNTED.
So 270 needs to be divided by 2! to eliminate overcounting handshakes.
Answer = 270 / 2! = 135.
I am not sure about my approach. Could any one shed some light on that. Really appreciate.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13330
Location: United States (CA)

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
30 Jan 2018, 12:46
Hi All, These types of question can often be solved with some basic notetaking and some 'brute force' math. I'm going to refer to the employees as... AAA BBB CCC DDD EEE FFF Each of the "A" employees will shake hands with each of the BCDEF employees, giving us (3)(15) = 45 handshakes. Since each of the "B" employees have ALREADY shaken hands with the "A" employees, they'll then shake hands with the CDEF employees. This gives us (3)(12) = 36 additional handshakes. In that same way, the "C"s shake hands with each of the DEF employees, giving us (3)(9) = 27 more handshakes The "D"s shake hands with each of the EF employees, giving us (3)(6) = 18 more handshakes And the "E"s shake hands with each of the F employees, giving us (3)(3) = 9 more handshakes Total handshakes = 45 + 36 + 27 + 18 + 9 = 135 handshakes Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Senior Manager
Joined: 15 Oct 2017
Posts: 312
GMAT 1: 560 Q42 V25 GMAT 2: 570 Q43 V27 GMAT 3: 710 Q49 V39

In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
30 Jan 2018, 13:05
I don't know if my approach is right:
Total number of reps: 18 Total no of reps to shake hands with (excluding his/her own company reps and obviously his/her ownself): 15 Therefore, total number of handshakes: 18*15=270 But handshake already involves two reps, i.e. when A shook hands with B, B also shook hands with A. Thus, effective total: 270/2=135.
B.



Intern
Joined: 24 May 2018
Posts: 9

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
12 Oct 2018, 23:25
Select 2 out of 18= 153 Select 2 out of 3 = 3 Select 2 out of 3 for all 6 companies = 3* 6 = 18 153 18 = 135




Re: In a meeting of 3 representatives from each of 6 different companies, &nbs
[#permalink]
12 Oct 2018, 23:25






