Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 09:00

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

m07 #27

Author Message
Senior Manager
Joined: 11 Dec 2008
Posts: 479
Location: United States
GMAT 1: 760 Q49 V44
GPA: 3.9
Followers: 40

Kudos [?]: 207 [1] , given: 12

Show Tags

27 Jul 2009, 21:17
1
KUDOS
3
This post was
BOOKMARKED
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

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

[Reveal] Spoiler: OE
Chairmen shake hands 10*7=70 with business executives times. Business executives shake hands with each other 10 C 2 times or 45 times. The total is 115 .

Can someone explain to me why its 10 C 2?
SVP
Joined: 29 Aug 2007
Posts: 2476
Followers: 70

Kudos [?]: 774 [4] , given: 19

Show Tags

28 Jul 2009, 07:18
4
KUDOS
2
This post was
BOOKMARKED
bipolarbear 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?

144
131
115
90
45

Can someone explain to me why its 10 C 2?

10 business executives shakes hands with other 9 business executives in 10c2 ways = 45 ways
10c2 = 9+8+7+6+5+4+3+2+1 = 45

First executive shakes hands with remaining 9 executives
Second executive shakes hands with remaining 8 executives
Third executive shakes hands with remaining 7 executives
Fourth executive shakes hands with remaining 6 executives
Fifth executive shakes hands with remaining 5 executives
Sixth executive shakes hands with remaining 4 executives
Seventh executive shakes hands with remaining 3 executives
Eighth executive shakes hands with remaining 2 executives
Nineth executive shakes hands with remaining 1 executives
Tenth executive already shakes hands with all 9 executives.

7 chairmen each shake hands with all 10 executive in 10x7 - 70 ways

Total handshakes = 45+70 = 115
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Senior Manager
Joined: 11 Dec 2008
Posts: 479
Location: United States
GMAT 1: 760 Q49 V44
GPA: 3.9
Followers: 40

Kudos [?]: 207 [0], given: 12

Show Tags

28 Jul 2009, 07:24
Oh... thank you. I read the question as "shakes hands with every other business executive" as shaking hands with alternating executives 2, 4, 6, 8, 10... which clearly did not make sense. +1 for you
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2786
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 238

Kudos [?]: 1727 [7] , given: 235

Show Tags

11 Jul 2010, 04:14
7
KUDOS
1
This post was
BOOKMARKED
Another method

17 c 2 - 7 c 2 = 115

17 c 2 = total number of hand shakes between 17 people
7 c 2 = total number of hand shakes between chairmen
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Joined: 07 Jul 2010
Posts: 1
Followers: 0

Kudos [?]: 1 [1] , given: 0

Show Tags

10 Aug 2010, 07:31
1
KUDOS
Here's how I did it:

#ways to select 1 businessman = 10
#ways to select another businessman = 9

#handshakes between businessmen only = 10x9/2 = 45 (We divide by 2 since order does not matter)

Scenario 2: businessman shakes hand with a chairman only
#was to select 1 businessman = 10
#ways to select 1 chairman = 7
#handshakes between businessmen and chairmen = 10x7/2 = 35

Scenario 3: chairman shakes hand with a businessman only.
#ways to select 1 chairman = 7
# was to select a businessman = 10
#handshakes between chairmen only = 7x10/2 = 35

Total handshakes = 45 + 35 + 35 = 115
Intern
Joined: 23 Jul 2010
Posts: 18
Location: New York
Schools: Booth, Columbia, Ross, Kellogg
Followers: 0

Kudos [?]: 10 [1] , given: 12

Show Tags

10 Aug 2010, 20:46
1
KUDOS
1
This post was
BOOKMARKED
here it is :
It takes 2 persons for one hand shake.
there are total 10 E + 7 C = 17 persons.
so total number of handshakes possible is 17C2.

The question is trying to confuse you by putting two different conditions.

17 C2 is possible when all people shakes hand with each other. But from the second condition , no chairman shakes hand with other chairman but executive.. so 7 persons are not shaking hands among themselves. So 7C2 cases must be subtracted.

Final Answer 17C2 - 7C2 = 115
Manager
Joined: 20 Jul 2010
Posts: 77
Followers: 5

Kudos [?]: 72 [0], given: 32

Show Tags

11 Aug 2010, 02:54
Here is my version of explanation:

If we have 3 people (Ex: P1, P2, P3), then the possible different shakehands are:
(P1, P2)(P1,P3) (P2,P3)

If we have 4 people (Ex: P1, P2, P3, P4), then the possible different shakehands are:
(P1, P2)(P1,P3) (P1,P4) (P2, P3) (P2, P4) (P3, P4) = Choosing 2 from 4, i.e, 4C2

If each business executive shakes the hand of every other business executive ... possible ways for this scenario are: 10C2=45

and every chairman once ... possible ways for this scenario are: 10 * 7 = 70

and each chairman shakes the hand of each of the business executives but not the other chairmen ....This is already covered as part of 10C2

So, Total: 45 + 70 = 115

Cheers!
Ravi
Current Student
Joined: 07 May 2010
Posts: 731
Followers: 14

Kudos [?]: 89 [0], given: 66

Show Tags

11 Aug 2010, 08:03
I thought of it a different way...
First i broke up the people into 2 groups execs and chairmen
first the chairmen they each shake the 10 execs hands only.....10x7=70
next the execs:
they shake in sets of 2 10C2 (taking out permutations) = 45

45+70 = 115

Best
_________________
Manager
Joined: 12 Jul 2010
Posts: 65
Followers: 1

Kudos [?]: 2 [0], given: 3

Show Tags

13 Aug 2010, 00:16
Its C.

10 Executives 7 Chairman

10 executives among themselves shake hands 9+8+7+6+5+4+3+2+1 = 45 times
7 chairman shakes hands with 10 executives 7*10 = 70 times

So total handshakes = 45 + 70 = 115
Manager
Joined: 20 Nov 2010
Posts: 221
Followers: 4

Kudos [?]: 32 [0], given: 38

Show Tags

11 Aug 2011, 05:45
Good question. C is the answer.
17C2 - 7C2 = 115
_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MGMAT 6 650 (51,31) on 31/8/11
MGMAT 1 670 (48,33) on 04/9/11
MGMAT 2 670 (47,34) on 07/9/11
MGMAT 3 680 (47,35) on 18/9/11
GMAT Prep1 680 ( 50, 31) on 10/11/11

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Manager
Joined: 16 Feb 2011
Posts: 54
Followers: 3

Kudos [?]: 26 [0], given: 0

Show Tags

11 Aug 2011, 06:58
10C2 +10x7=45+70=115
Senior Manager
Joined: 19 Oct 2010
Posts: 262
Location: India
GMAT 1: 560 Q36 V31
GPA: 3
Followers: 7

Kudos [?]: 80 [0], given: 27

Show Tags

04 Sep 2011, 00:13

as per the above mentioned problem, here is the reasoning that will follow:
Let's assume each business exec. is assigned an alphabet A thru J
Let's assume each chairman is assigned a number 1 thru 7.

Now, starting with A (counting all busi. execs. and chairmen), A would shake 16 unique hands in all.
Next, proceeding to B (counting all busi. execs. and chairmen), B would shake 15 unique hands in all (A would be excluded).
Similarly, calculate this for C, D, E, F, G, H, I and J. Since the chairmen do not exchange handshakes among themselves, this isn't required.

Now add all the unique handshakes to find the total:
16+15+14+13+12+11+10+9+8+7 = 115
_________________

petrifiedbutstanding

Manager
Joined: 14 Mar 2011
Posts: 85
Followers: 1

Kudos [?]: 43 [0], given: 21

Show Tags

04 Sep 2011, 02:57
70 handshakes from Directors to Executive
10C2 for handshakes with Exe to Exe = 45 Total Handshakes = 70+45 = 115
Manager
Joined: 12 Sep 2010
Posts: 225
Followers: 2

Kudos [?]: 26 [0], given: 24

Show Tags

25 Jan 2012, 23:39
bipolarbear wrote:
Oh... thank you. I read the question as "shakes hands with every other business executive" as shaking hands with alternating executives 2, 4, 6, 8, 10... which clearly did not make sense. +1 for you

That was exactly how I interpreted the question. Now I get it.
Math Expert
Joined: 02 Sep 2009
Posts: 38903
Followers: 7739

Kudos [?]: 106208 [3] , given: 11611

Show Tags

26 Jan 2012, 02:56
3
KUDOS
Expert's post
2
This post was
BOOKMARKED
bipolarbear 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

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

[Reveal] Spoiler: OE
Chairmen shake hands 10*7=70 with business executives times. Business executives shake hands with each other 10 C 2 times or 45 times. The total is 115 .

Can someone explain to me why its 10 C 2?

Approach #1:
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).

$$Desired=Total-restriction=C^2_{17}-C^2_{7}=115$$.

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

_________________
Manager
Joined: 18 Jan 2012
Posts: 51
Location: United States
Followers: 4

Kudos [?]: 92 [2] , given: 26

Show Tags

15 Aug 2012, 05:34
2
KUDOS
Lets think of it this way.
It takes 2 to tango, or in this case shake hands
The total number of shakehand greetings = The total Nr of 2 person groups that we can form.

10 Execs
Nr of 2 person groups we can form = 10 C 2 = 45

7 Chairman and 10 Execs
Nr of 2 person groups we can form, which INCLUDE 1 chairman and 1 Exec
7 C 1 x 10 C 1 = 70 ..

Total 70 + 45 = 115

Here is an easy way to calculate permutations and combinations without using the formula
n P M = n x n-1 x n-2 ...m times
10 P 3 = 10 x 9 x 8 ( i.e 3 terms)
11 P 6 = 11 x 10 x 9 x 8 x 7 x 6 (i.e 6 terms)

n C m = (n x n-1 x n-2 ...m times) / 1 x 2 .. m terms
10 C 2 = 10 x 9 / 1 x 2
11 C 8 = 11 C 3 = 11 x 10 x 9 / 1 x 2 x 3

_________________
IT TAKES QUITE A BIT OF EFFORT TO POST DETAILED RESPONSES.
YOUR KUDOS IS VERY MUCH APPRECIATED

_________________

-----------------------------------------------------------------------------------------------------
IT TAKES QUITE A BIT OF TIME AND TO POST DETAILED RESPONSES.
YOUR KUDOS IS VERY MUCH APPRECIATED

-----------------------------------------------------------------------------------------------------

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1381
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 178

Kudos [?]: 1464 [0], given: 62

Show Tags

15 Aug 2012, 06:14
My take:
There are 10 executives and 7 chairman..
The given condition is that each executive can shake with another person only once.
That stands to (10*9)/2 +(10*7)/2 which equals 80.
I have divided the above by 2 to reduce redundancy, i.e., A shakes with B is the same thing as B shakes with A.
Moreover, each chair doesn't shakes with other chairman but the executives.
Hence (7*10)/2=35.
Total=80+35=115.
C
_________________
Intern
Status: Looking for High GMAT Score
Joined: 19 May 2012
Posts: 36
Location: India
Concentration: Strategy, Marketing
WE: Marketing (Internet and New Media)
Followers: 0

Kudos [?]: 6 [0], given: 58

Show Tags

15 Aug 2012, 23:34
10c2+10*7

very common kind of question
_________________

“The best time to plant a tree was 20 years ago. The second best time is now.” – Chinese Proverb

Manager
Joined: 14 Jun 2012
Posts: 65
Followers: 0

Kudos [?]: 13 [1] , given: 1

Show Tags

29 Aug 2012, 07:55
1
KUDOS
It took me a significantly longer time than 2 mins and in the end I kind of guessed C. Honestly it was more of just a guess and not an educated guess.

Going through the explanations, it has helped me realize where I was going wrong. I was considering the total handshakes by a business executive as (9+7) and was summing this for a total of 7 executives. The explanations above really helped me understand my mistake. (Total handshakes - between chairmen) was a real smart way to go about the solution.
_________________

My attempt to capture my B-School Journey in a Blog : tranquilnomadgmat.blogspot.com

There are no shortcuts to any place worth going.

Intern
Joined: 10 Aug 2013
Posts: 22
GPA: 4
WE: Military Officer (Transportation)
Followers: 0

Kudos [?]: 9 [0], given: 10

Show Tags

15 Aug 2013, 09:34
17C2 - 7C2 =136-21=115.
Hand shake question always refer to a combination problems.
If X men in a group then XC2 hand shakes.
clearly hand shake haven't occurred between 7 so subtract 7C2.
Re: m07 #27   [#permalink] 15 Aug 2013, 09:34

Go to page    1   2    Next  [ 27 posts ]

Similar topics Replies Last post
Similar
Topics:
20 M07 #2 15 30 Oct 2012, 05:32
3 m07 q33 10 29 Nov 2013, 02:35
6 m07 #22 19 12 May 2014, 09:33
M07: Q25 10 02 Jun 2011, 10:17
1 m07q18 16 11 Jul 2010, 05:44
Display posts from previous: Sort by

m07 #27

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO 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®.