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

It is currently 20 Oct 2018, 06:51

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 conference of 3 delegates from each of 8 different organizations,

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50004
In a conference of 3 delegates from each of 8 different organizations,  [#permalink]

Show Tags

New post 02 Oct 2018, 02:08
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

55% (02:24) correct 45% (01:49) wrong based on 31 sessions

HideShow timer Statistics

In a conference of 3 delegates from each of 8 different organizations, each delegate shook hands with every person other than those from his or her own organization. How many handshakes took place in the conference?

(A) 48
(B) 96
(C) 252
(D) 270
(E) 504

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
S
Joined: 19 Oct 2013
Posts: 314
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User
In a conference of 3 delegates from each of 8 different organizations,  [#permalink]

Show Tags

New post Updated on: 04 Oct 2018, 23:02
Bunuel wrote:
In a conference of 3 delegates from each of 8 different organizations, each delegate shook hands with every person other than those from his or her own organization. How many handshakes took place in the conference?

(A) 48
(B) 96
(C) 252
(D) 270
(E) 504


This is a tricky one.

1,1,1
2,2,2
3,3,3 etc..

If the delegates from group (1) shake hands with each from group (2) this means 3 hand shakes for each of the delegates from Group 1.

Since delegates from group (1) will shake hands with all delegates from 2,3,4,5,6,7,8

It means each member in group 1 will shake hands 21 times. (8-1)*3 = 21

8-1 = 7 to exclude the hand shakes from their group.

Since each shakes hand once it means per group they have 21*3 = 63

There are 8 groups so it means 63*8 = 504
But this double-counts.

So we divide it by 2 we get 504/2 = 252.


Answer choice C.

Another way would be to say

A member of group one gets 21 hand shakes
A member of group two gets 18
A member of group three gets 15
A member of group four gets 12
A member of group five gets 9
A member of group six gets 6
A member of group seven gets 3
And a member of group 8 gets 0.

Adding all the above numbers we get 84

And 84*3 = 252

Here the 3 is to account for 3 members in the group.

I hope it is clear

Posted from my mobile device

Originally posted by Salsanousi on 03 Oct 2018, 15:20.
Last edited by Salsanousi on 04 Oct 2018, 23:02, edited 1 time in total.
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)
Re: In a conference of 3 delegates from each of 8 different organizations,  [#permalink]

Show Tags

New post 04 Oct 2018, 19:31
1
Bunuel wrote:
In a conference of 3 delegates from each of 8 different organizations, each delegate shook hands with every person other than those from his or her own organization. How many handshakes took place in the conference?

(A) 48
(B) 96
(C) 252
(D) 270
(E) 504


We are given that there are 3 representatives from 8 different companies. So, there are a total of 24 representatives.

If every representative were to shake hands with all other representatives (meaning all 24 reps would shake hands), this would happen in the following number of ways:

24C2 = (24 x 23)/2! = 12 x 23 = 276 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 8 companies, this would occur 8 x 3 = 24 times.

Thus, the number of ways for the reps to shake hands with every person not from his or her own company is 276 - 24 = 252 ways.

Alternate Solution:

Each of the 3 x 8 = 24 representative will shake hands with 24 - 3 = 21 people since representatives within the same organization won’t shake hands with each other. Thus, 24 x 21 will be equal to twice the number of handshakes that took place in the organization, since each handshake is counted twice (each handshake is counted once for each person involved in the handshake, hence the double count). Then, there were 24 x 21 x (1/2) = 12 x 21 = 252 handshakes that took place in the organization.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Manager
avatar
B
Joined: 24 Dec 2017
Posts: 119
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: In a conference of 3 delegates from each of 8 different organizations,  [#permalink]

Show Tags

New post 04 Oct 2018, 23:08
1 company = 3 delegates
Total companies present = 8
Total number of delegates = 24

In the question, each delegate shook hands with every person other than those from his or her own organization
=>1 delegate will shake hands with 21 other delegates
=>Total = 21 handshakes

There are a total of 24 delegates and therefore the total number of handshakes = 21x24 = 504 Handshakes(This includes the repetition of handshakes)
So we should divide it by 2
=>504/2
=>252

Hence C is the answer
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India
Re: In a conference of 3 delegates from each of 8 different organizations,  [#permalink]

Show Tags

New post 05 Oct 2018, 00:08
Bunuel wrote:
In a conference of 3 delegates from each of 8 different organizations, each delegate shook hands with every person other than those from his or her own organization. How many handshakes took place in the conference?

(A) 48
(B) 96
(C) 252
(D) 270
(E) 504


Consider the 3 delegates of the first org. Each of the 3 delegates will shake hands with delegates from the other 7 organisations i.e. with 7*3 people.
Consider the next team of delegates from the second org. Each of the 3 delegates will shake hands with delegates of other 6 orgs (since they have already shaken hands with the first org delegates) i.e. with 6*3 = 18 people.
So we see the pattern: No of handshakes = 3*(21 + 18 + ... + 3)

The underlined is an AP. Its sum = (No of terms)*(First term + last term)/2

Sum = 3 * 7*(21 + 3)/2 = 3*84 = 252

Answer (C)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

GMAT Club Bot
Re: In a conference of 3 delegates from each of 8 different organizations, &nbs [#permalink] 05 Oct 2018, 00:08
Display posts from previous: Sort by

In a conference of 3 delegates from each of 8 different organizations,

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.