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

It is currently 16 Oct 2019, 22:30

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

M07-27

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58390
M07-27  [#permalink]

Show Tags

New post 16 Sep 2014, 00:35
2
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (02:11) correct 26% (02:34) wrong based on 78 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?

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

_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58390
Re M07-27  [#permalink]

Show Tags

New post 16 Sep 2014, 00:35
1
1
Official Solution:

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


Approach 1:

Total number of handshakes possible between \(10+7=17\) people (with no restrictions) is the number 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).

\(\text{Desired}=\text{Total}-\text{Restriction}=C^2_{17}-C^2_{7}=115\).

Approach 2:

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


Answer: C
_________________
Manager
Manager
avatar
Joined: 08 Feb 2014
Posts: 201
Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
WE: Analyst (Commercial Banking)
Re: M07-27  [#permalink]

Show Tags

New post 10 Nov 2014, 09:30
1
For those using manhattan's notation:

10!/(2!8!) = 45

10*70 = 70

45+70=115
Intern
Intern
avatar
Joined: 13 Sep 2013
Posts: 6
Re: M07-27  [#permalink]

Show Tags

New post 18 Nov 2014, 09:40
1
I have a doubt on this question. It says that each business executive shakes the hand of every other B. Executive. From this statement, I understand that each B. Executvies shakes hands with 4 of the other business executives. Can someone explain me why we are considering that all B. Executives shake hands with each other?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58390
Re: M07-27  [#permalink]

Show Tags

New post 18 Nov 2014, 09:44
tatianamontllonch wrote:
I have a doubt on this question. It says that each business executive shakes the hand of every other B. Executive. From this statement, I understand that each B. Executvies shakes hands with 4 of the other business executives. Can someone explain me why we are considering that all B. Executives shake hands with each other?


Every other does not mean here every 2nd.
_________________
Intern
Intern
avatar
Joined: 13 Sep 2013
Posts: 6
Re: M07-27  [#permalink]

Show Tags

New post 18 Nov 2014, 09:48
2
Sorry for my ignorance, but how I am suposse to know that in this case every other, does not mean every 2nd? 'Cos in that case the answer is 90 and it is also on of the options :(
Senior Manager
Senior Manager
User avatar
Joined: 12 Aug 2015
Posts: 280
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Re: M07-27  [#permalink]

Show Tags

New post 04 Oct 2015, 09:12
amt88 wrote:
Sorry for my ignorance, but how I am suposse to know that in this case every other, does not mean every 2nd? 'Cos in that case the answer is 90 and it is also on of the options :(


i agree, "each other" should eliminate ambiguity
_________________
KUDO me plenty
Intern
Intern
avatar
Joined: 05 Aug 2015
Posts: 40
Re: M07-27  [#permalink]

Show Tags

New post 10 Nov 2015, 21:55
shasadou wrote:
amt88 wrote:
Sorry for my ignorance, but how I am suposse to know that in this case every other, does not mean every 2nd? 'Cos in that case the answer is 90 and it is also on of the options :(


i agree, "each other" should eliminate ambiguity


Also got this problem wrong because of "every other" wording. Really should consider changing........
_________________
Working towards 25 Kudos for the Gmatclub Exams - help meee I'm poooor
Manager
Manager
User avatar
Joined: 05 Jul 2015
Posts: 93
Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40
GPA: 3.3
Re: M07-27  [#permalink]

Show Tags

New post 25 Feb 2016, 13:49
2
I understood it the way it was intended but I can see how some people could be confused.

The way I solved was by multiplying execs by chairmen = 70

Then I thought, the first Exec can shake 9 other executives. Then the next one can shake 8, 7,6,5,4,3,2,1 which adds to 45.

70+45 = 115
Intern
Intern
User avatar
Joined: 08 Jul 2015
Posts: 40
GPA: 3.8
WE: Project Management (Energy and Utilities)
Reviews Badge
Re: M07-27  [#permalink]

Show Tags

New post 27 May 2016, 22:39
DJ1986 wrote:
I understood it the way it was intended but I can see how some people could be confused.

The way I solved was by multiplying execs by chairmen = 70

Then I thought, the first Exec can shake 9 other executives. Then the next one can shake 8, 7,6,5,4,3,2,1 which adds to 45.

70+45 = 115


I used the same approach as well :-D
_________________
[4.33] In the end, what would you gain from everlasting remembrance? Absolutely nothing. So what is left worth living for?
This alone: justice in thought, goodness in action, speech that cannot deceive, and a disposition glad of whatever comes, welcoming it as necessary, as familiar, as flowing from the same source and fountain as yourself. (Marcus Aurelius)
Manager
Manager
avatar
Joined: 21 Sep 2015
Posts: 73
Location: India
GMAT 1: 730 Q48 V42
GMAT 2: 750 Q50 V41
Reviews Badge
M07-27  [#permalink]

Show Tags

New post 02 Jul 2016, 23:41
I think this is a poor-quality question due to the question being worded ambiguously
"each business executive shakes the hand of each of the business executives" is much clearer
_________________
Appreciate any KUDOS given ! :)
Intern
Intern
avatar
B
Joined: 07 Oct 2016
Posts: 13
M07-27  [#permalink]

Show Tags

New post 19 Oct 2016, 11:53
"business executive shakes the hand of every other business executive AND every chairman once"-

I multipled 45 and 70 because of AND

How do we come to know whether we add or multiply ????

Pl someone help

Thanks in advance
Intern
Intern
avatar
B
Joined: 21 Oct 2014
Posts: 4
Location: Ukraine
GMAT 1: 680 Q48 V35
GPA: 3.05
GMAT ToolKit User
Re: M07-27  [#permalink]

Show Tags

New post 03 Jan 2017, 05:41
Some people may find it easier to remember and use a shortcut formula for a number of handshakes:
n(n-1)/2, where n is the total number of people who are going to shake hands.
It is basically derived from the combinations formula n Choose 2.
Current Student
avatar
B
Joined: 24 Nov 2016
Posts: 16
Location: United States
Concentration: Finance, Sustainability
GMAT 1: 680 Q46 V38
GPA: 3.43
WE: Project Management (Other)
M07-27  [#permalink]

Show Tags

New post 24 Jan 2017, 17:33
I am glad to know I am not the only one who fell into the ambiguity trap of this question. If someone is unable to write in a clear and clean way, shouldn`t be writing question at all, or at least should rely on a editor in order to avaid such gross mistake. I spent a long time trying to figure out this question because someone did a poor job writting it. I hope real GMAT Test will be more professional to this regard. And can someone please take care of correcting this mistake in order not to frustrate other people in the future? Thank you!!
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
M07-27  [#permalink]

Show Tags

New post 01 May 2018, 05:15
1
Another way to approach this is: When a group shakes hands within itself, then the number of handshakes are counted twice as when A shakes hands with B, B is also shaking hands with A. Hence, easy way is to divide the total number of handshakes by 2 within a group to avoid double counting and count total number of handshakes between different groups by simple multiplication. Here, it will be [(10*9)/2] + 10*7 = (90/2) + 70 = 115.
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2400
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
M07-27  [#permalink]

Show Tags

New post 14 Oct 2018, 07:29
Bunuel wrote:
Official Solution:

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


Approach 1:

Total number of handshakes possible between \(10+7=17\) people (with no restrictions) is the number 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).

\(\text{Desired}=\text{Total}-\text{Restriction}=C^2_{17}-C^2_{7}=115\).

Approach 2:

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


Answer: C


Number of handshakes for first business executive = 16 ( Business executive one shakes hand with 9 other business executives and 7 chairmen)
Number of handshakes for second business executive =15 ( the handshake with the first executive is excluded here since it has been already counted for first business executive)

Similarly, Number of handshakes for tenth business executive= 7 ( the handshakes with other 9 executives are excluded here since those have already been counted)

Total number of handshakes = 10/2 *(16+7) = 5*23 = 115 (Sum of AP= total number of terms/2 * (first term+last term) )

Answer C
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Senior Manager
Senior Manager
User avatar
P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 434
Premium Member
Re: M07-27  [#permalink]

Show Tags

New post 11 Jul 2019, 11:35
Bunuel 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


Step 1: Execs shake hands everyone
Ways to choose * Choices = 10 execs * 16 (they don't shake their own hand) = 160

Step 2: chairmen shake hands with execs
Ways * Choices = 7 * 10 = 70

160+70 = 230, now we divide by 2 to get rid of the extras (there is no difference between person A shaking hands with B or person B shaking hands with A) 230/2 = 115.
Intern
Intern
avatar
B
Joined: 04 Sep 2016
Posts: 16
Re: M07-27  [#permalink]

Show Tags

New post 16 Aug 2019, 06:29
I have a lot of challenges with this sort of questions. In fact, combination and permutation type of questions. Can anyone please direct me to links on GMATCLUB that I can use to learn the fundamentals and to answer questions?


Bunuel wrote:
Official Solution:

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


Approach 1:

Total number of handshakes possible between \(10+7=17\) people (with no restrictions) is the number 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).

\(\text{Desired}=\text{Total}-\text{Restriction}=C^2_{17}-C^2_{7}=115\).

Approach 2:

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


Answer: C


Posted from my mobile device
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58390
Re: M07-27  [#permalink]

Show Tags

New post 16 Aug 2019, 06:37
1
gbengoose wrote:
I have a lot of challenges with this sort of questions. In fact, combination and permutation type of questions. Can anyone please direct me to links on GMATCLUB that I can use to learn the fundamentals and to answer questions?


Bunuel wrote:
Official Solution:

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


Approach 1:

Total number of handshakes possible between \(10+7=17\) people (with no restrictions) is the number 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).

\(\text{Desired}=\text{Total}-\text{Restriction}=C^2_{17}-C^2_{7}=115\).

Approach 2:

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


Answer: C


Posted from my mobile device


21. Combinatorics/Counting Methods



For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread


Hope it helps.
_________________
GMAT Club Bot
Re: M07-27   [#permalink] 16 Aug 2019, 06:37
Display posts from previous: Sort by

M07-27

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

Moderators: chetan2u, Bunuel






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