Last visit was: 19 Jul 2025, 14:38 It is currently 19 Jul 2025, 14:38
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 July 2025
Posts: 102,625
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,625
Kudos: 742,781
 [22]
Kudos
Add Kudos
21
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
vitaliyGMAT
Joined: 13 Oct 2016
Last visit: 26 Jul 2017
Posts: 297
Own Kudos:
843
 [4]
Given Kudos: 40
GPA: 3.98
Posts: 297
Kudos: 843
 [4]
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
General Discussion
User avatar
RMD007
Joined: 03 Jul 2016
Last visit: 08 Jun 2019
Posts: 236
Own Kudos:
190
 [2]
Given Kudos: 80
Status:Countdown Begins...
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE:Information Technology (Consulting)
Products:
Schools: IIMB
GMAT 1: 580 Q48 V22
Posts: 236
Kudos: 190
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
AR15J
Joined: 21 Aug 2016
Last visit: 15 May 2024
Posts: 215
Own Kudos:
Given Kudos: 145
Location: India
GPA: 3.9
WE:Information Technology (Computer Software)
Products:
Posts: 215
Kudos: 158
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Ruchi for writing this "There are 6 delegations, each contains 3 representatives." Now I can comprehend the ques.
(5*3*3*6)/2=135
User avatar
shashank1tripathi
Joined: 12 Jun 2016
Last visit: 22 Nov 2017
Posts: 21
Own Kudos:
Given Kudos: 18
Location: India
Concentration: Entrepreneurship, Finance
GPA: 3.76
WE:Information Technology (Computer Software)
Posts: 21
Kudos: 17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think answer should be D.
Total number of members: 6 * 3 = 18
Total number of handshakes(including among same delegations) : 18C2 = 153
Now, Total handshakes among same delegations = 6 * 3C2 = 18
So, Answer = 153 - 18 = 135
User avatar
US09
Joined: 15 Oct 2017
Last visit: 06 Apr 2021
Posts: 248
Own Kudos:
286
 [1]
Given Kudos: 338
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Products:
GMAT 3: 710 Q49 V39
Posts: 248
Kudos: 286
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
There is another way to solve this: each member shakes hand with other members and not with herself, therefore each member shakes hands with 15 members. So, 18 members shake hands with 15 others= 18*15. But when one member shakes hand with other, the other will not be required to repeat the same (since, shaking hands is a two way thing, does not need to be repeated once done between two members. Hence, 18*15/2= 135.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 18 Jul 2025
Posts: 21,145
Own Kudos:
26,205
 [2]
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,145
Kudos: 26,205
 [2]
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
Six three-representative delegations attend an international conference. The representatives shake hands when they are introduced to one another. How many handshakes are possible if each delegate shakes hands only once with every other attendant except with those of his/her delegation?

A) 36
B) 72
C) 90
D) 135
E) 388

We are given that there are 3 representatives from 6 different delegations. 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 delegation, 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 delegation is 153 - 18 = 135 ways.

Alternate Solution:

Let’s count the total number of handshakes. Since each of the 6 x 3 = 18 representatives shake hands with 5 x 3 = 15 other representatives, this makes 18 x 15 = 270 handshakes. However, we counted each handshake twice, once for each of the parties involved in the handshake. Therefore, the number of handshakes that take place is 270 / 2 = 135.

Answer: D
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 19 Jul 2025
Posts: 8,353
Own Kudos:
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy)
GMAT Focus 1: 545 Q79 V79 DI73
Posts: 8,353
Kudos: 4,833
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Six three-representative delegations attend an international conference. The representatives shake hands when they are introduced to one another. How many handshakes are possible if each delegate shakes hands only once with every other attendant except with those of his/her delegation?

A) 36
B) 72
C) 90
D) 135
E) 388

total handshakes would 18c3 ; 153
total hand shakes if done within each group ; 3c2 *6 ; 18
so total handshakes shakes hands only once with every other attendant except with those of his/her delegation ; 153-18 ; 135
IMO D
User avatar
TestPrepUnlimited
Joined: 17 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,226
Own Kudos:
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,226
Kudos: 1,067
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Six three-representative delegations attend an international conference. The representatives shake hands when they are introduced to one another. How many handshakes are possible if each delegate shakes hands only once with every other attendant except with those of his/her delegation?

A) 36
B) 72
C) 90
D) 135
E) 388

If every single person took turns shaking hands with all other people, we would have 18 * 15 handshakes in total (15 because "each delegate shakes hands only once with every other attendant except for those of his/her delegation"). However, with this product we would have any two people (of different delegation) shaking hands with each other twice, e.g. A shakes hands with B and B shakes hands with A are both counted with this method. We only need one of each combination to happen therefore we divide by 2 to get 9*15 = 135.

Ans: D
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 19 Jul 2025
Posts: 5,703
Own Kudos:
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
GMAT 1: 690 Q50 V34
Posts: 5,703
Kudos: 5,238
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given: Six three-representative delegations attend an international conference. The representatives shake hands when they are introduced to one another.
Asked: How many handshakes are possible if each delegate shakes hands only once with every other attendant except with those of his/her delegation?

Every delegate will shake hands with = 5*3 = 15 delegates
Since there are 18 delegates, total handshakes = 18*15 = 135*2

Since each handshake is counted twice, total handshakes = 135

IMO D
avatar
Aravind04
Joined: 25 Nov 2021
Last visit: 08 Nov 2022
Posts: 23
Own Kudos:
Given Kudos: 893
Location: India
Posts: 23
Kudos: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1. Total Handshakes possible = N(N-1)/2 ==> (18*17)/2 ==> 153

2. In one group there can be 2 hand shakes from one person to other 2 people say delegation one has ABC as members
a handshakes with AB,AC so other 2 also handshake with others with in delegation

3. total 6 hand shakes with in delegation divided by 2 will eliminate counting twice
hence==> 3 hand shakes per delegation * 6 delegations = 18 hand shakes which should not be counted

4. Total -handshakes with in delegations ==>153-18==> 135
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,450
Own Kudos:
Posts: 37,450
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Math Expert
102625 posts
PS Forum Moderator
698 posts