Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Aug 2014, 05:02

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

All of the stocks on the over the counter market are

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 27 Jan 2012
Posts: 10
GMAT 1: 710 Q45 V41
Followers: 0

Kudos [?]: 2 [0], given: 4

All of the stocks on the over the counter market are [#permalink] New post 27 Jan 2012, 12:35
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (01:49) correct 31% (00:56) wrong based on 205 sessions
All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be desgnated with these codes?

A. 2 (26)^5
B. 26(26)^4
C. 27(26)^4
D. 26(26)^5
E. 27(26)^5
[Reveal] Spoiler: OA
Expert Post
7 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19083
Followers: 3399

Kudos [?]: 24841 [7] , given: 2692

Re: Tricky combinatorics question [#permalink] New post 27 Jan 2012, 12:38
7
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be desgnated with these codes?
A. 2 (26)^5
B. 26(26)^4
C. 27(26)^4
D. 26(26)^5
E. 27(26)^5

In 4-digit code {XXXX} each digit can take 26 values (as there are 26 letters), so total # of 4-digits code possible is 26^4;

The same for 5-digit code {XXXXX} again each digit can take 26 values (26 letters), so total # of 5-digits code possible is 26^5;

Total: 26^4+26^5=26^4(1+26)=27*26^4.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Manager
Manager
avatar
Joined: 17 Oct 2010
Posts: 81
Followers: 1

Kudos [?]: 71 [1] , given: 26

GMAT Tests User
Re: All of the stocks on the over the counter market are [#permalink] New post 23 Jun 2012, 02:30
1
This post received
KUDOS
Important point to note here is that letters are not distinct , i.e we can have a code as aaaa or aaaaa for 4 or 5 letter words respectively.


This question is similar to the question
if-a-code-word-is-defined-to-be-a-sequence-of-different-126652.html
In which we have selected 4 letters from 10 and 5 letters from 10 but in this case the letters have to be distinct.

so using P^{10}_{4} and P^{10}_{5}
we get \frac{10!}{6!} and \frac{10!}{5!}

But cannot we use the same logic here to select 4 letters from 26 or 5 letters from 26, why?... because the letters are not distinct ( letters can be repeated ) and we cannot use the general permutation formula when there is repetition .

so we cannot use P^{26}_{4} + P^{26}_{5}


if this question were each four letter code and 5 letter code are made of distinct elements then the answer, I think could be
P^{26}_{4} + P^{26}_{5}. 4 distinct letters can be selected from 26 or 5 distinct letters can be selected from 26 to make the 4 digit codes or 5 digit codes .

so if "distinct " is not mentioned then we automatically should assume that there can be repetitions .

So in this question since no distinct word is mentioned , we can assume letters can we repeated to form the codes.Unlike the sum in the link above.

Hope this will prevent many people from wondering why we are solving two very similar questions in two very different ways. like I myself was wondering for a while before this eureka moment

if Anyone can add or verify or correct the reasoning that I have used It would certainly help.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 409
Followers: 2

Kudos [?]: 56 [1] , given: 82

Re: All of the stocks on the over the counter market are [#permalink] New post 23 Jun 2012, 10:24
1
This post received
KUDOS
26^4+26^5 when we have "OR" word in sentence then when we add two posibilities and wen we have and word ..we multiple those posibilties
26^4(1+26)=27*26^4
so ans C..
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Senior Manager
Senior Manager
avatar
Joined: 02 Sep 2012
Posts: 292
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Followers: 3

Kudos [?]: 70 [0], given: 99

Re: All of the stocks on the over the counter market are [#permalink] New post 05 May 2013, 06:14
a-4-letter-code-word-consists-of-letters-a-b-and-c-if-the-59065.html

in the link posted above also contains a similar question of 4 letter code where A,B,C,A - two A's are repeating so we are using a formula 4 !/2 !
here also we are repeating the same letters tats why we are 26 ^4 for a letter code .But i should be 26 ^4 /4 ! na?

please help me i am getting confused..When should i use the principle n!/ no# repeating letters and when i should not?
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Intern
Intern
avatar
Joined: 23 Apr 2013
Posts: 22
Followers: 0

Kudos [?]: 12 [0], given: 1

Re: All of the stocks on the over the counter market are [#permalink] New post 05 May 2013, 08:00
skamal7 wrote:
http://gmatclub.com/forum/a-4-letter-code-word-consists-of-letters-a-b-and-c-if-the-59065.html

in the link posted above also contains a similar question of 4 letter code where A,B,C,A - two A's are repeating so we are using a formula 4 !/2 !
here also we are repeating the same letters tats why we are 26 ^4 for a letter code .But i should be 26 ^4 /4 ! na?

please help me i am getting confused..When should i use the principle n!/ no# repeating letters and when i should not?



Here each letter can come any number of times. i.e a 4 letter code can be aaaa.

But in the link provided by you, due to the restrictions imposed by the question, such liberty is not allowed there. There each letter should appear atleast once... leaving only 1 letter to repeat. Hence the difference.

Hope you understood it :)
Senior Manager
Senior Manager
avatar
Joined: 02 Sep 2012
Posts: 292
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Followers: 3

Kudos [?]: 70 [0], given: 99

Re: All of the stocks on the over the counter market are [#permalink] New post 05 May 2013, 08:06
So you mean to say that if there is no restriction then we will use the method followed for this question but if there comes restrictions such as same letters should repeat twice or thrice we have to use n!/identical objects!

Is my understanding correct ? :?
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Intern
Intern
avatar
Joined: 23 Apr 2013
Posts: 22
Followers: 0

Kudos [?]: 12 [0], given: 1

Re: All of the stocks on the over the counter market are [#permalink] New post 05 May 2013, 15:29
skamal7 wrote:
So you mean to say that if there is no restriction then we will use the method followed for this question but if there comes restrictions such as same letters should repeat twice or thrice we have to use n!/identical objects!

Is my understanding correct ? :?


Yep. Almost.
The restriction in the question you provided is that only the given set of alphabets can be used.
Another example of that can be like " How many 5 digit code words can be formed using the letters {A,A,B,B,B}"
The answer to this is 5!/(2!*3!)

Hope you got your answer. :)
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2182
Followers: 184

Kudos [?]: 36 [0], given: 0

Premium Member
Re: All of the stocks on the over the counter market are [#permalink] New post 19 May 2014, 02:34
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

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 268
Followers: 0

Kudos [?]: 10 [0], given: 23

Re: All of the stocks on the over the counter market are [#permalink] New post 23 Aug 2014, 09:43
Joy111 wrote:
Important point to note here is that letters are not distinct , i.e we can have a code as aaaa or aaaaa for 4 or 5 letter words respectively.


This question is similar to the question
if-a-code-word-is-defined-to-be-a-sequence-of-different-126652.html
In which we have selected 4 letters from 10 and 5 letters from 10 but in this case the letters have to be distinct.

so using P^{10}_{4} and P^{10}_{5}
we get \frac{10!}{6!} and \frac{10!}{5!}

But cannot we use the same logic here to select 4 letters from 26 or 5 letters from 26, why?... because the letters are not distinct ( letters can be repeated ) and we cannot use the general permutation formula when there is repetition .

so we cannot use P^{26}_{4} + P^{26}_{5}


if this question were each four letter code and 5 letter code are made of distinct elements then the answer, I think could be
P^{26}_{4} + P^{26}_{5}. 4 distinct letters can be selected from 26 or 5 distinct letters can be selected from 26 to make the 4 digit codes or 5 digit codes .

so if "distinct " is not mentioned then we automatically should assume that there can be repetitions .

So in this question since no distinct word is mentioned , we can assume letters can we repeated to form the codes.Unlike the sum in the link above.

Hope this will prevent many people from wondering why we are solving two very similar questions in two very different ways. like I myself was wondering for a while before this eureka moment

if Anyone can add or verify or correct the reasoning that I have used It would certainly help.


You hit on a topic that i was wondering about. Are you saying that we cannot use the 10C4 + 10C5 but we CAN use 10P4 + 10P5 because the permutation formula let's you account for repetitions?
Re: All of the stocks on the over the counter market are   [#permalink] 23 Aug 2014, 09:43
    Similar topics Author Replies Last post
Similar
Topics:
1 All of the stocks on the over-the-counter market are designa ashiima 1 15 Dec 2011, 17:58
1 Experts publish their posts in the topic All of the stocks on the over-the-counter market are designa Macsen 4 16 Nov 2011, 19:18
1 Experts publish their posts in the topic All the stocks on the over-the-counter market are designated Folaa3 31 20 Aug 2005, 07:28
1 Experts publish their posts in the topic All of the stocks on the over the counter market are kt00381n 7 30 Aug 2009, 12:36
All of the stocks on the over-the-counter market are misterJJ2u 3 20 Jan 2007, 23:14
Display posts from previous: Sort by

All of the stocks on the over the counter market are

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.