Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 27 Mar 2017, 19:44

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# All of the stocks on the over the counter market are

Author Message
TAGS:

### Hide Tags

Intern
Joined: 27 Jan 2012
Posts: 10
GMAT 1: 710 Q45 V41
Followers: 0

Kudos [?]: 27 [1] , given: 4

All of the stocks on the over the counter market are [#permalink]

### Show Tags

27 Jan 2012, 13:35
1
KUDOS
30
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:56) correct 28% (01:22) wrong based on 701 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 37619
Followers: 7406

Kudos [?]: 99716 [10] , given: 11035

### Show Tags

27 Jan 2012, 13:38
10
KUDOS
Expert's post
10
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: $$26^4+26^5=26^4(1+26)=27*26^4$$.

_________________
Manager
Joined: 18 Oct 2010
Posts: 79
Followers: 1

Kudos [?]: 173 [2] , given: 26

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

23 Jun 2012, 03:30
2
KUDOS
2
This post was
BOOKMARKED
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.
Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 202 [1] , given: 82

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

23 Jun 2012, 11:24
1
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
Joined: 02 Sep 2012
Posts: 259
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Followers: 5

Kudos [?]: 187 [0], given: 99

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

05 May 2013, 07:14
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
Joined: 23 Apr 2013
Posts: 22
Followers: 0

Kudos [?]: 19 [1] , given: 1

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

05 May 2013, 09:00
1
KUDOS
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
Joined: 02 Sep 2012
Posts: 259
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Followers: 5

Kudos [?]: 187 [0], given: 99

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

05 May 2013, 09:06
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
Joined: 23 Apr 2013
Posts: 22
Followers: 0

Kudos [?]: 19 [0], given: 1

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

05 May 2013, 16:29
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!)

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14478
Followers: 609

Kudos [?]: 174 [0], given: 0

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

19 May 2014, 03:34
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.
_________________
Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 59 [0], given: 23

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

23 Aug 2014, 10:43
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?
Current Student
Joined: 11 Oct 2013
Posts: 124
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31
Followers: 1

Kudos [?]: 54 [0], given: 137

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

25 Oct 2014, 11:44
Bunuel wrote:
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: $$26^4+26^5=26^4(1+26)=27*26^4$$.

In this case, wouldn't there be a possibility of 2 tickets having the same code? If no, can you please explain! Thanks
_________________

Its not over..

Math Expert
Joined: 02 Sep 2009
Posts: 37619
Followers: 7406

Kudos [?]: 99716 [0], given: 11035

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

26 Oct 2014, 07:07
Expert's post
2
This post was
BOOKMARKED
swanidhi wrote:
Bunuel wrote:
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: $$26^4+26^5=26^4(1+26)=27*26^4$$.

In this case, wouldn't there be a possibility of 2 tickets having the same code? If no, can you please explain! Thanks

Which two codes could possibly be the same? It would be better to try with an easier example: try to count the number of 3 digit codes using 2 letters. You should get 2^3.

For more practice, check Constructing Numbers, Codes and Passwords in our Speciall Questions Directory.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14478
Followers: 609

Kudos [?]: 174 [0], given: 0

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

08 Nov 2015, 02:05
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.
_________________
Senior Manager
Joined: 20 Aug 2015
Posts: 398
Location: India
GMAT 1: 760 Q50 V44
Followers: 27

Kudos [?]: 228 [1] , given: 10

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

09 Nov 2015, 00:41
1
KUDOS
Expert's post
Murmeltier wrote:
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

The first thing to note in these questions is whether we are allowed to repeat the variables or not.
Since here, nothing about repetition is mentioned, we can safely assume that we can repeat the variables.

4 Letter Code: _ _ _ _
The first place can have 26 alphabets.
The second place can also have 26 alphabets, since we can repeat.
Similarly for 3rd and 4th.
Hence total codes = 26*26*26*26 = $$26^4$$

5 Letter Code: _ _ _ _ _
By the above logic,
Total codes = $$26^5$$

Since we are asked the 4 letter codes OR the 5 letter codes,

Total codes = $$26^4 + 26^5$$ = $$26^4(26 + 1)$$ = $$26^4*27$$

Option C
_________________

Reach out to us at bondwithus@gmatify.com

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14478
Followers: 609

Kudos [?]: 174 [0], given: 0

Re: All of the stocks on the over the counter market are [#permalink]

### Show Tags

13 Nov 2016, 09:13
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.
_________________
Re: All of the stocks on the over the counter market are   [#permalink] 13 Nov 2016, 09:13
Similar topics Replies Last post
Similar
Topics:
4 The value of a "Tin-Rin" stock in the stock market decreased by 15% in 7 21 Jun 2016, 03:10
When the stock market opened yesterday, the price of a share 2 31 Mar 2012, 21:16
3 All of the stocks on the over-the-counter market are designa 3 15 Dec 2011, 18:58
2 All of the stocks on the over-the-counter market are designa 4 16 Nov 2011, 20:18
1 All of the stocks on the over the counter market are 7 30 Aug 2009, 13:36
Display posts from previous: Sort by