GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Oct 2019, 00:33

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In a meeting of 3 representatives from each of 6 different companies,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
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

New post Updated on: 10 Apr 2016, 10:12
4
60
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (02:04) correct 36% (01:57) wrong based on 542 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

Originally posted by surupab on 10 Apr 2016, 08:22.
Last edited by Bunuel on 10 Apr 2016, 10:12, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7959
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 10 Apr 2016, 09:29
47
1
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?
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 = 153-18= 135

B
_________________
Most Helpful Community Reply
Intern
Intern
User avatar
S
Joined: 21 Jan 2016
Posts: 46
Location: India
GMAT 1: 640 Q44 V34
WE: Manufacturing and Production (Manufacturing)
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 10 Apr 2016, 09:02
21
1
3
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
General Discussion
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7959
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 10 Apr 2016, 09:26
11
6
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 =135

B
_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4003
Location: Canada
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 10 Apr 2016, 10:34
26
10
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
Image
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1873
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 11 Jul 2016, 21:22
7
1
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
Intern
avatar
B
Joined: 07 Jun 2016
Posts: 31
GPA: 3.8
WE: Supply Chain Management (Manufacturing)
GMAT ToolKit User
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 12 Oct 2016, 19:05
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 =135

B


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
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 626
Location: India
In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 21 May 2017, 19:51
Top Contributor
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 Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 23 May 2017, 17:21
3
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
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star 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
Intern
avatar
B
Joined: 30 Mar 2016
Posts: 37
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 18 Jan 2018, 02:55
1
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
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15262
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 30 Jan 2018, 13:46
Hi All,

These types of question can often be solved with some basic note-taking 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.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Senior Manager
Senior Manager
avatar
P
Joined: 15 Oct 2017
Posts: 295
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Reviews Badge
In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 30 Jan 2018, 14:05
1
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
Intern
avatar
B
Joined: 24 May 2018
Posts: 8
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 13 Oct 2018, 00:25
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
Intern
avatar
B
Joined: 13 May 2019
Posts: 7
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 05 Jun 2019, 15:49
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.
Senior Manager
Senior Manager
User avatar
G
Joined: 17 Jul 2018
Posts: 428
Premium Member Reviews Badge
Re: In a meeting of 3 representatives from each of 6 different companies,  [#permalink]

Show Tags

New post 19 Jul 2019, 07:51
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 18C2- (6x3)
Ans 135
GMAT Club Bot
Re: In a meeting of 3 representatives from each of 6 different companies,   [#permalink] 19 Jul 2019, 07:51
Display posts from previous: Sort by

In a meeting of 3 representatives from each of 6 different companies,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne