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:
64% (02:02) correct 36% (01:58) wrong based on 699 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: 8295

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
_________________




Intern
Joined: 21 Jan 2016
Posts: 46
Location: India
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
_________________




GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4551
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



Math Expert
Joined: 02 Aug 2009
Posts: 8295

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
_________________



SVP
Joined: 06 Nov 2014
Posts: 1865

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



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2801

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
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 30 Mar 2016
Posts: 36

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.



Senior Manager
Joined: 15 Oct 2017
Posts: 292
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.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16322
Location: United States (CA)

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
16 Mar 2020, 11:42
Kritisood wrote: Could someone explain why 15c2 is wrong? which scenario am I missing in this? Hi Kritisood, To start, there are 18 total people; using 15c2 would assume that you're taking every "pair" of possible people from 15 total people, which is not what the prompt describes. In addition, since people are NOT supposed to shake hands with other members of the same company that they work for, you can't just choose "any 2" people to shake hands  it has to be 2 people from DIFFERENT companies. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 07 Jun 2016
Posts: 30
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: 619
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 Magical Logicians https://magicallogicianssatgmatgre.business.siteHolistic and Holy Approach



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16322
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
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 24 May 2018
Posts: 8

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



Intern
Joined: 13 May 2019
Posts: 7

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
05 Jun 2019, 14:49
There are 18 people:
Organize these 18 people into 6 groups of 3 ( each group of 3 is from the same company)
Then you chose 2 groups from the 6 groups. (6C2)
Then from the 2 groups there are 3 ways to pick pairs. Have to remember that Person A, Person B handshake is the same as Person B Person A handshake. so it is 3*6C2 = 135.



Sloan MIT School Moderator
Joined: 17 Jul 2018
Posts: 891

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
19 Jul 2019, 06:51
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 SUCH QUESTIONS JUST DEPEND ON STRIKING Lets look at this one the easy way All shook hands  the people who didn't will give you the result. That is 18 C2 (6x3) Ans 135
_________________
https://consultingbusinessconqueror.business.site/?m=truehttps://kartiknimbalkaralp.wixsite.com/website Want free Admissions consulting? Free Admissions and GMAT consulting GMAT Club special No spams No bullshit; Purely FACT BASED SOCIAL SERVICE



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6061
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
26 Dec 2019, 11:11
Total handshakes 18c2 Restriction 3c2×6:18 18c218; 135 IMO B 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 Posted from my mobile device



Intern
Joined: 14 Sep 2016
Posts: 10

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
21 Jan 2020, 19:41
can someone please explain why the total # of handshakes is 18C2. Why are we choosing 2 handshakes? What is the logic via this approach?



Math Expert
Joined: 02 Aug 2009
Posts: 8295

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
21 Jan 2020, 19:56
abalodi wrote: can someone please explain why the total # of handshakes is 18C2. Why are we choosing 2 handshakes? What is the logic via this approach? Since any handshake requires two people, we are counting different ways 2 people can be selected out of 18 people.
_________________



Intern
Joined: 14 Sep 2016
Posts: 10

Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
Show Tags
21 Jan 2020, 19:57
That seems all to obvious but now it all makes sense. Appreciate the help!
Posted from my mobile device




Re: In a meeting of 3 representatives from each of 6 different companies,
[#permalink]
21 Jan 2020, 19:57



Go to page
1 2
Next
[ 22 posts ]



