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

It is currently 12 Dec 2018, 13:12

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

There are y different travelers who each have a choice of va

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

Hide Tags

Manager
Manager
User avatar
Joined: 22 Jul 2009
Posts: 168
There are y different travelers who each have a choice of va  [#permalink]

Show Tags

New post 22 Sep 2009, 15:59
1
20
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

45% (01:39) correct 55% (01:24) wrong based on 322 sessions

HideShow timer Statistics

There are y different travelers who each have a choice of vacationing at one of n different destinations. What is the probability that all y travelers will end up vacationing at the same destination?

A. 1/n!
B. n/n!
C. 1/n^y
D. 1/n^(y-1)
E. n/y^n

Source: Manhattan GMAT Archive (tough problems set).doc

_________________

Please kudos if my post helps.

Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8665
Location: Pune, India
Re: PS, Probability - There are y different travelers ...  [#permalink]

Show Tags

New post 10 May 2011, 05:52
5
6
powerka wrote:
There are y different travelers who each have a choice of vacationing at one of n different destinations. What is the probability that all y travelers will end up vacationing at the same destination?
a) 1/n!
b) n/n!
c) 1/n^y
d) 1/n^(y-1)
e) n/y^n

Source: Manhattan GMAT Archive (tough problems set).doc



There are 2 ways to handle a question with variables. Using logic which I endorse and plugging in numbers which I discuss for those situations where you run out of time or are thoroughly confused or are exhausted. I will take both though the logic has pretty much been discussed above.

The first traveler has n options to choose from (n destinations). The moment he chooses one of those n, every one else has to take the same destination. So number of favorable outcomes = n
If there were no constraints, each of the y travelers could choose any one of the n destinations. So total number of combinations = n*n*... (y times)
\(Probability = \frac{n}{n^y} = \frac{1}{n^{y-1}}\)

Plugging in numbers:
Say y = 1 and n = 2 (1 traveler, 2 places)
What is the probability that all travelers will go to the same place? 1 of course since there is only one traveler. Where ever he goes is the place where all travelers are! Plug it in options. Only options b and d give 1 when you plug in y = 1 and n = 2.
Say y = 2 and n = 2 (2 travelers, 2 places)
They could either be together at a place or at two different places so probability of being together is 1/2. Plug n = 2, y = 2 in options b and d. Only option d gives you 1/2.
_________________

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 >

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 11 Sep 2009
Posts: 129
Re: PS, Probability - There are y different travelers ...  [#permalink]

Show Tags

New post 22 Sep 2009, 16:15
10
2
The answer is D: 1/n^(y-1).

The simplest way to look at it is to assume that the first traveler picks a place. All the remaining travelers (given as y-1) now need to pick the same place for vacation.

As a result the probability is equivalent to (1/n) for each traveler to pick that same spot as the original traveler, which has to happen (y-1) times.

\(P = \frac{1}{n}*\frac{1}{n}*...*\frac{1}{n}\) (y-1) times

\(P = {\frac{1}{n}}^{(y-1)}\)
General Discussion
Manager
Manager
avatar
Joined: 11 Aug 2008
Posts: 126
Re: PS, Probability - There are y different travelers ...  [#permalink]

Show Tags

New post Updated on: 25 Oct 2009, 08:32
But I end up choose the 1/n^y ways

Originally posted by ngoctraiden1905 on 21 Oct 2009, 20:08.
Last edited by ngoctraiden1905 on 25 Oct 2009, 08:32, edited 1 time in total.
Manager
Manager
User avatar
Joined: 22 Jul 2009
Posts: 168
Re: PS, Probability - There are y different travelers ...  [#permalink]

Show Tags

New post 22 Oct 2009, 05:25
4
1
winning outcomes = n (and not 1)
total outcomes = n^y
=> n/n^y = 1/n^(y-1)
_________________

Please kudos if my post helps.

VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1033
Re: PS, Probability - There are y different travelers ...  [#permalink]

Show Tags

New post 09 May 2011, 00:12
Cool solution.
1/n^(y-1).
Retired Moderator
avatar
B
Joined: 16 Nov 2010
Posts: 1425
Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: PS, Probability - There are y different travelers ...  [#permalink]

Show Tags

New post 10 May 2011, 05:34
6
2
Prob that traveler 1 will choose 1st place(any particular place) out n places = 1/n

Prob that traveler 2 will choose same place out n places = 1/n
......


Total = 1/n * ... 1/n (y times)

= 1/n^y

But this can happen for all of the n places.

So Prob = n/(n^y) = 1/n^(y-1)

Answer - D
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Joined: 20 Jan 2014
Posts: 145
Location: India
Concentration: Technology, Marketing
GMAT ToolKit User
Re: There are y different travelers who each have a choice of va  [#permalink]

Show Tags

New post 22 Sep 2014, 04:34
powerka wrote:
There are y different travelers who each have a choice of vacationing at one of n different destinations. What is the probability that all y travelers will end up vacationing at the same destination?

A. 1/n!
B. n/n!
C. 1/n^y
D. 1/n^(y-1)
E. n/y^n

Source: Manhattan GMAT Archive (tough problems set).doc



Excellent question. Totally Stumped.
_________________

Consider +1 Kudos Please :)

Manager
Manager
avatar
G
Joined: 28 Jul 2016
Posts: 134
Premium Member
Re: There are y different travelers who each have a choice of va  [#permalink]

Show Tags

New post 07 Apr 2017, 06:48
AKProdigy87 wrote:
The answer is D: 1/n^(y-1).

The simplest way to look at it is to assume that the first traveler picks a place. All the remaining travelers (given as y-1) now need to pick the same place for vacation.

As a result the probability is equivalent to (1/n) for each traveler to pick that same spot as the original traveler, which has to happen (y-1) times.

\(P = \frac{1}{n}*\frac{1}{n}*...*\frac{1}{n}\) (y-1) times

\(P = {\frac{1}{n}}^{(y-1)}\)

thank you for sharing nice explanation :)
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9139
Premium Member
Re: There are y different travelers who each have a choice of va  [#permalink]

Show Tags

New post 22 Apr 2018, 03:59
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: There are y different travelers who each have a choice of va &nbs [#permalink] 22 Apr 2018, 03:59
Display posts from previous: Sort by

There are y different travelers who each have a choice of va

  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®.