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

It is currently 16 Aug 2018, 22:21

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

Six people are on an elevator that stops at exactly 6 floors

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

Hide Tags

Intern
Intern
avatar
Joined: 14 Feb 2012
Posts: 2
Six people are on an elevator that stops at exactly 6 floors  [#permalink]

Show Tags

New post 19 Feb 2012, 06:02
1
15
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

49% (01:07) correct 51% (01:02) wrong based on 440 sessions

HideShow timer Statistics

Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor?

(A) 6!/6^6
(B) 6^6/6!
(C) 6/6!
(D) 6/6^6
(E) 1/6^6
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47946
Re: Six people  [#permalink]

Show Tags

New post 19 Feb 2012, 06:11
6
2
caliber23 wrote:
Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor?

(A) 6!/6^6
(B) 6^6/6!
(C) 6/6!
(D) 6/6^6
(E) 1/6^6


Each person out of 6 has 6 options, hence total # of outcomes is 6^6;

Favorable outcomes will be 6!, which is # of ways to assign 6 different buttons to 6 people:
1-2-3-4-5-6 (floors)
A-B-C-D-E-F (persons)
B-A-C-D-E-F (persons)
B-C-A-D-E-F (persons)
...
So basically # of arrangements of 6 distinct objects: 6!.

P=favorable/total=6!/6^6

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Intern
Intern
avatar
B
Joined: 09 Apr 2013
Posts: 40
Location: United States (DC)
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 750 Q50 V41
GPA: 3.55
WE: General Management (Non-Profit and Government)
Re: Six Six people are on an elevator that stops at exactly 6  [#permalink]

Show Tags

New post 07 Jun 2013, 07:52
5
1
Gwydion wrote:
Hi, could you please tell me the mistake in the following logic?

First person entering pushes one button, it doesn't matter which: p=1
Second person pushes a button that has not been pressed before. Since one is already pushed, only 5 remain: p=5/6
Same logic for third person: p=4/6
.
.
.

This leaves us with The probability of all pushing a different button of: 1*5/6*4/6*4/6*2/6*1/6 or 5!/6^5

Where's the mistake?


Expanding on Gwydion's post - it is true that p=1, but because the answers all have 6 in them, the first person should be written as p=6/6 to make it easier to see the answer:

First person walks in and can push any button (6/6)
Probability that second person will press any of the remaining 5 buttons (5/6)
Probability that third person will press any of the remaining 4 buttons (4/6)
Probability that fourth person will press any of the remaining 3 buttons (3/6)
Probability that fifth person will press either of the remaining 2 buttons (2/6)
Probability that sixth person will press the remaining button (1/6)

\(\frac{6}{6} * \frac{5}{6} * \frac{4}{6} * \frac{3}{6} * \frac{2}{6} * \frac{1}{6} = \frac{6*5*4*3*2*1}{6*6*6*6*6*6} = \frac{6!}{6^6}\)

Answer is A
General Discussion
Intern
Intern
avatar
Joined: 17 Aug 2011
Posts: 22
GMAT 1: 750 Q48 V44
GPA: 3.8
WE: Management Consulting (Consulting)
Re: Six Six people are on an elevator that stops at exactly 6  [#permalink]

Show Tags

New post 19 Feb 2012, 06:55
Hi, could you please tell me the mistake in the following logic?

First person entering pushes one button, it doesn't matter which: p=1
Second person pushes a button that has not been pressed before. Since one is already pushed, only 5 remain: p=5/6
Same logic for third person: p=4/6
.
.
.

This leaves us with The probability of all pushing a different button of: 1*5/6*4/6*4/6*2/6*1/6 or 5!/6^5

Where's the mistake?
Manager
Manager
avatar
Joined: 10 Jan 2010
Posts: 161
Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GPA: 3
WE: Consulting (Telecommunications)
Re: Six Six people are on an elevator that stops at exactly 6  [#permalink]

Show Tags

New post 19 Feb 2012, 06:57
Totol possibilities: 6^6 (Each person may push each level the button)

First floor: 6 person
second floor: 5 person
...
= 6!

Possibility: 6!/6^6 --> A
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47946
Re: Six Six people are on an elevator that stops at exactly 6  [#permalink]

Show Tags

New post 19 Feb 2012, 11:48
Gwydion wrote:
Hi, could you please tell me the mistake in the following logic?

First person entering pushes one button, it doesn't matter which: p=1
Second person pushes a button that has not been pressed before. Since one is already pushed, only 5 remain: p=5/6
Same logic for third person: p=4/6
.
.
.

This leaves us with The probability of all pushing a different button of: 1*5/6*4/6*4/6*2/6*1/6 or 5!/6^5

Where's the mistake?


There is no mistake: 6!/6^6=(5!*6)/(6^5*6)=5!/6^5, the same answers.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47946
Re: Six people are on an elevator that stops at exactly 6 floors  [#permalink]

Show Tags

New post 07 Jun 2013, 07:03
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on probability problems: math-probability-87244.html

All DS probability problems to practice: search.php?search_id=tag&tag_id=33
All PS probability problems to practice: search.php?search_id=tag&tag_id=54

Tough probability questions: hardest-area-questions-probability-and-combinations-101361.html

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 16 May 2015
Posts: 14
Re: Six people are on an elevator that stops at exactly 6 floors  [#permalink]

Show Tags

New post 21 May 2015, 06:15
Does this logic work ?

Assuming we are calculating the options for that one person
we use the number of floors are the options.
Person A presses at the ground floor has 6 options, then 5 options as so on as he goes up. so 6*5*4*3*2*1 = 6!
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 1894
Re: Six people are on an elevator that stops at exactly 6 floors  [#permalink]

Show Tags

New post 21 May 2015, 06:51
1
shallow9323 wrote:
Does this logic work ?

Assuming we are calculating the options for that one person
we use the number of floors are the options.
Person A presses at the ground floor has 6 options, then 5 options as so on as he goes up. so 6*5*4*3*2*1 = 6!


Dear shallow9323

Yes, your logic is right.

Calculating Favorable Cases (where each person gets down at a different floor)

Options for Person A = Number of floors that the elevator stops at = 6
Options for Person B = 5 and so on

So total number of ways in which the 6 people can each get down at a different floor = 6*5*4*3*2*1 = 6!

To give you additional practice for this logic, here's a follow-up question:

Three people are on an elevator that goes to 6 floors. What is the probability that each person will get out of the elevator at a different floor?


Best Regards

Japinder
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Intern
avatar
Joined: 16 May 2015
Posts: 14
Re: Six people are on an elevator that stops at exactly 6 floors  [#permalink]

Show Tags

New post 21 May 2015, 07:10
1
EgmatQuantExpert wrote:
shallow9323 wrote:
Does this logic work ?

Assuming we are calculating the options for that one person
we use the number of floors are the options.
Person A presses at the ground floor has 6 options, then 5 options as so on as he goes up. so 6*5*4*3*2*1 = 6!


Dear shallow9323

Yes, your logic is right.

Calculating Favorable Cases (where each person gets down at a different floor)

Options for Person A = Number of floors that the elevator stops at = 6
Options for Person B = 5 and so on

So total number of ways in which the 6 people can each get down at a different floor = 6*5*4*3*2*1 = 6!

To give you additional practice for this logic, here's a follow-up question:

Three people are on an elevator that goes to 6 floors. What is the probability that each person will get out of the elevator at a different floor?


Best Regards

Japinder


Thank you.

The practice one is the answer 6*5*4=120 ?
Intern
Intern
User avatar
Joined: 16 Jan 2015
Posts: 49
Location: United States
Schools: Kellogg '17, ISB '17
GMAT Date: 05-20-2015
GPA: 3.06
WE: Business Development (Commercial Banking)
Re: Six people are on an elevator that stops at exactly 6 floors  [#permalink]

Show Tags

New post 21 May 2015, 07:19
Total no of fav cases-- 6p6

Total no of cases-- 6^6

so ans -- A = 6p6 / 6^6

:D
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 1894
Re: Six people are on an elevator that stops at exactly 6 floors  [#permalink]

Show Tags

New post 21 May 2015, 07:20
shallow9323 wrote:
EgmatQuantExpert wrote:
shallow9323 wrote:
Does this logic work ?

Assuming we are calculating the options for that one person
we use the number of floors are the options.
Person A presses at the ground floor has 6 options, then 5 options as so on as he goes up. so 6*5*4*3*2*1 = 6!


Dear shallow9323

Yes, your logic is right.

Calculating Favorable Cases (where each person gets down at a different floor)

Options for Person A = Number of floors that the elevator stops at = 6
Options for Person B = 5 and so on

So total number of ways in which the 6 people can each get down at a different floor = 6*5*4*3*2*1 = 6!

To give you additional practice for this logic, here's a follow-up question:

Three people are on an elevator that goes to 6 floors. What is the probability that each person will get out of the elevator at a different floor?


Best Regards

Japinder


Thank you.

The practice one is the answer 6*5*4=120 ?


Dear shallow9323

Yes, you got the number of favorable cases right :)

So, the probability of each person getting out at a different floor = \(\frac{(6*5*4)}{(6*6*6)}\) = \(\frac{5}{9}\)

Best,

Japinder
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Manager
avatar
Joined: 03 May 2013
Posts: 72
Re: Six people are on an elevator that stops at exactly 6 floors  [#permalink]

Show Tags

New post 03 Aug 2015, 23:59
Bunuel wrote:
caliber23 wrote:
Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor?

(A) 6!/6^6
(B) 6^6/6!
(C) 6/6!
(D) 6/6^6
(E) 1/6^6


HI Experts, it seems there is some problem with stem, it should be exactly one different person, otherwise 6c1/6 *6c1/6...6 times = 1 would be the ans
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7732
Premium Member
Re: Six people are on an elevator that stops at exactly 6 floors  [#permalink]

Show Tags

New post 15 Mar 2018, 10:05
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

Re: Six people are on an elevator that stops at exactly 6 floors &nbs [#permalink] 15 Mar 2018, 10:05
Display posts from previous: Sort by

Six people are on an elevator that stops at exactly 6 floors

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

Events & Promotions

PREV
NEXT


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®.