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

It is currently 17 Jan 2019, 13:39

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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

In how many ways can a person post 5 letters in 4 letter box

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

Hide Tags

 
Retired Moderator
avatar
B
Joined: 27 Aug 2012
Posts: 1088
Premium Member
In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 03 Feb 2013, 05:11
1
5
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (00:27) correct 27% (00:52) wrong based on 106 sessions

HideShow timer Statistics

In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 2^3
(B) 4^2
(C) 4^3
(D) 4^5
(E) 5^5

_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || GMAC's IR Prep Tool

Calling all Columbia (CBS) MBA Applicants: (2018 Intake) Class of 2020 !!! NEW !!!

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)

Manager
Manager
avatar
Joined: 02 Jan 2013
Posts: 57
GMAT 1: 750 Q51 V40
GPA: 3.2
WE: Consulting (Consulting)
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 03 Feb 2013, 06:55
1
Something is up with this question. Options (B) and (D) are exactly the same.

In my opinion, the correct solution for this is:

Arrange the 5 items in 4 different "baskets":
xxxxx|||

Total of 8!/(5!*3!) = 8.7 = 56

Now we can order these 5 items among themselves: 5! = 120 ways

Answer = 56*120 = 6720 IMO
Senior Manager
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 469
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 03 Feb 2013, 09:47
3
debayan222 wrote:
1.In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?


There are 4 places (ABCD) that need to be filled.
Letter 1 can be posted in either A, B, C, or D i.e. 4 ways
Letter 2 can be posted in either A, B, C, or D i.e. 4 ways
Letter 3 can be posted in either A, B, C, or D i.e. 4 ways
Letter 4 can be posted in either A, B, C, or D i.e. 4 ways
Letter 5 can be posted in either A, B, C, or D i.e. 4 ways

So the total no of ways in which 5 letters can be posted in 4 boxes are = 4 x 4 x 4 x 4 x 4 = 4 ^ 5

Thus the answer is D

Hope it helps.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Intern
Intern
User avatar
Joined: 08 Feb 2011
Posts: 11
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post Updated on: 04 Feb 2013, 08:45
Thanks Fameatop (1+)
After reading the problem again and realizing what the question was asking, your logic makes perfect sense.

Is caioguima's approach incorrect because we are counting certain letter box combos multiple times when we multiply by 5!?
Would caioguima's method be correct if the order of the letters in the boxes mattered?

Thanks to vips and debayan as well

Originally posted by holidayhero on 03 Feb 2013, 10:08.
Last edited by holidayhero on 04 Feb 2013, 08:45, edited 3 times in total.
Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 587
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
GMAT ToolKit User Premium Member Reviews Badge
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 03 Feb 2013, 10:17
debayan222 wrote:
1.In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?

Fameatop got it right.

For each letter the person has 4 options.
Thus 4*4*4*4*4=4^5=1024

Ans b and d are both correct. (Dude don't mind but watch for the source)
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

Retired Moderator
avatar
B
Joined: 27 Aug 2012
Posts: 1088
Premium Member
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 03 Feb 2013, 22:58
fameatop wrote:
debayan222 wrote:
1.In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?


There are 4 places (ABCD) that need to be filled.
Letter 1 can be posted in either A, B, C, or D i.e. 4 ways
Letter 2 can be posted in either A, B, C, or D i.e. 4 ways
Letter 3 can be posted in either A, B, C, or D i.e. 4 ways
Letter 4 can be posted in either A, B, C, or D i.e. 4 ways
Letter 5 can be posted in either A, B, C, or D i.e. 4 ways

So the total no of ways in which 5 letters can be posted in 4 boxes are = 4 x 4 x 4 x 4 x 4 = 4 ^ 5

Thus the answer is D

Hope it helps.


fameatop-You're correct...!Honestly I was having confusion with this...but it appears really easy :)
_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || GMAC's IR Prep Tool

Calling all Columbia (CBS) MBA Applicants: (2018 Intake) Class of 2020 !!! NEW !!!

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)

Retired Moderator
avatar
B
Joined: 27 Aug 2012
Posts: 1088
Premium Member
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 03 Feb 2013, 23:04
Vips0000 wrote:
debayan222 wrote:
1.In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?

Fameatop got it right.

For each letter the person has 4 options.
Thus 4*4*4*4*4=4^5=1024

Ans b and d are both correct. (Dude don't mind but watch for the source)


Vips0000-You got it too...!
And the source-it's one of the questions in IIM CAT materials of a CAT prep companies...unfortunately it's due to lack of proof-reading you know !

Not much we can do dude but just to point it out... :wink:
_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || GMAC's IR Prep Tool

Calling all Columbia (CBS) MBA Applicants: (2018 Intake) Class of 2020 !!! NEW !!!

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3331
Location: Canada
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 21 Apr 2018, 06:11
Top Contributor
bagdbmba wrote:
In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5


Take the task of distributing the 5 letters and break it into stages.

Stage 1: Select a box for the 1st letter to go into.
There are 4 available boxes, so we can complete stage 1 in 4 ways

Stage 2: Select a box for the 2nd letter to go into.
There are 4 available boxes, so we can complete stage 2 in 4 ways

Stage 3: Select a box for the 3rd letter to go into.
There are 4 available boxes, so we can complete stage 3 in 4 ways

Stage 4: Select a box for the 4th letter to go into.
There are 4 available boxes, so we can complete stage 4 in 4 ways

Stage 5: Select a box for the 5th letter to go into.
There are 4 available boxes, so we can complete stage 5 in 4 ways

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus distribute all 5 letters) in (4)(4)(4)(4)(4) ways (= 4⁵ ways)

Answer: D

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS



_________________

Test confidently with gmatprepnow.com
Image

Intern
Intern
avatar
B
Joined: 03 Apr 2018
Posts: 10
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 08 May 2018, 10:12
I need help in my thought process:
why dont be solve it by slot method

- - - - for four letter box. and then , 1st place has 5 letters tro choose from then 2nd letter box had 4 letters to choose from?
5*4*3*2 ?
Please help me clear this doubt.
Manager
Manager
avatar
B
Joined: 13 Dec 2018
Posts: 50
Location: India
GPA: 3.94
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 17 Dec 2018, 22:16
Each letter has 4 options.
So, total no of ways = 4 x 4 x 4 x 4 x 4 = 4^5
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India
Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

Show Tags

New post 17 Dec 2018, 22:22
bagdbmba wrote:
In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?


Check out different cases of unfair distribution in these two posts on the Veritas blog:
https://www.veritasprep.com/blog/2011/1 ... inatorics-–-part-1/
https://www.veritasprep.com/blog/2011/1 ... s-part-ii/
_________________

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 >

GMAT Club Bot
Re: In how many ways can a person post 5 letters in 4 letter box &nbs [#permalink] 17 Dec 2018, 22:22
Display posts from previous: Sort by

In how many ways can a person post 5 letters in 4 letter box

  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®.