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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

10 business executives and 7 chairmen meet at a conference [#permalink]

Show Tags

16 Jan 2012, 10:51

1

This post received KUDOS

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

71% (01:26) correct
29% (01:46) wrong based on 281 sessions

HideShow timer Statistics

10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?

10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?

144 131 115 90 45 what is the quickest way to solve it. help please

Total # of handshakes possible between 10+7=17 people (with no restrictions) is # of different groups of two we can pick from these 10+7=17 people (one handshake per pair), so \(C^2_{17}\). The same way: # of handshakes between chairmen \(C^2_{7}\) (restriction).

Or direct way: # of handshakes between executives \(C^2_{10}\) plus 10*7 (as each executive shakes the hand of each 7 chairmen): \(C^2_{10}+10*7=115\).

Re: 10 business executives and 7 chairmen meet at a conference [#permalink]

Show Tags

19 Jan 2012, 00:06

1

This post received KUDOS

Business Executives (BE) can shake hands with every other business executives and chairman (C).

BE and C - 10 *7 =70 Be vs BE - 10c2 = 10!/(2!*(10-2)!)= 45 So total hand shakes = 70 +45 =115 Since chairman shakes hands only with business executive, it is enough if we compute that once

Re: 10 business executives and 7 chairmen meet at a conference [#permalink]

Show Tags

28 Dec 2012, 01:25

1

This post received KUDOS

manalq8 wrote:

10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?

A. 144 B. 131 C. 115 D. 90 E. 45

How many times to select 2 persons to handshake from 10 execs? \(\frac{10!}{2!8!} = 45\) How many handshakes by 10 exec to all chairment each? \(10*7 = 70\) How many times each chair to handshake 10 execs? This has already been counted above.

Re: 10 business executives and 7 chairmen meet at a conference [#permalink]

Show Tags

24 Nov 2013, 04:41

Well this is a long shot method, but if you are like me and have problem calculating permutations and combination this may help:

Now the question requires us to calculate the total number of handshakes. The total number of hand shakes is equal (Unique)Hand Shakes made by the Executives + (Unique) Hand Shakes Made by the CEOs

So to Calculate the Unique Handshakes made by the executives, the following calculations need to be made:

1st Executive shakes hand with Executives (A)= 9, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 16 2nd Executive shakes hand with Executives (A)= 8, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 15 (The number has decreased because his hand shake with the 1st executive cannot be recounted) 3rd Executive shakes hand with Executives (A)= 7, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 14 4th Executive shakes hand with Executives (A)= 6, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 13 5th Executive shakes hand with Executives (A)= 5, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 12 6th Executive shakes hand with Executives (A)= 4, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 11 7th Executive shakes hand with Executives (A)= 3, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 10 8th Executive shakes hand with Executives (A)= 2, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 09 9th Executive shakes hand with Executives (A)= 1, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 08 10th Executive shakes hand with Executives (A)= 0, He shakes hands with CEOs (B)= 7, Total Hand Shakes=A+B = 07

Now, the Unique Handshakes made by the CEOs is 0. Because all their handshakes are with the Executives, that have been covered earlier. So the total handshakes in the given situation are equal to the sum of the unique handshakes made by the executives which are 115. And our answer is C.

Re: 10 business executives and 7 chairmen meet at a conference [#permalink]

Show Tags

12 Dec 2013, 23:48

1)10C2=45 (ways of picking 2 people out of 10 business executives, which equals to number of their handshakes) 2)10*7=70 (every business executive has 7 chairmen to shake hands) 3)70+45=115

Re: 10 business executives and 7 chairmen meet at a conference [#permalink]

Show Tags

10 Aug 2015, 01:04

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.
_________________

Re: 10 business executives and 7 chairmen meet at a conference [#permalink]

Show Tags

27 Jan 2017, 03:44

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.
_________________