Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 27 Jan 2012
Posts: 10

All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
27 Jan 2012, 13:35
Question Stats:
75% (01:30) correct 25% (01:57) wrong based on 1064 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 designated with these codes? A. \(2(26)^5\) B. \(26(26)^4\) C. \(27(26)^4\) D. \(26(26)^5\) E. \(27(26)^5\)
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 50002

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
27 Jan 2012, 13:38




Manager
Joined: 18 Oct 2010
Posts: 76

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
23 Jun 2012, 03:30
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 ifacodewordisdefinedtobeasequenceofdifferent126652.htmlIn 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: 341

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
23 Jun 2012, 11:24
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 !



Manager
Joined: 02 Sep 2012
Posts: 212
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07252013
GPA: 3.83
WE: Architecture (Computer Hardware)

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
05 May 2013, 07:14
a4lettercodewordconsistsoflettersabandcifthe59065.htmlin 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?



Intern
Joined: 23 Apr 2013
Posts: 21

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
05 May 2013, 09:00
skamal7 wrote: http://gmatclub.com/forum/a4lettercodewordconsistsoflettersabandcifthe59065.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



Manager
Joined: 11 Oct 2013
Posts: 109
Concentration: Marketing, General Management

Re: All of the stocks on the over the counter market are designated by eit
[#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 4digit code {XXXX} each digit can take 26 values (as there are 26 letters), so total # of 4digits code possible is 26^4;
The same for 5digit code {XXXXX} again each digit can take 26 values (26 letters), so total # of 5digits code possible is 26^5;
Total: \(26^4+26^5=26^4(1+26)=27*26^4\).
Answer: C. 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: 50002

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
26 Oct 2014, 07:07
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 4digit code {XXXX} each digit can take 26 values (as there are 26 letters), so total # of 4digits code possible is 26^4;
The same for 5digit code {XXXXX} again each digit can take 26 values (26 letters), so total # of 5digits code possible is 26^5;
Total: \(26^4+26^5=26^4(1+26)=27*26^4\).
Answer: C. 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.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 20 Aug 2015
Posts: 391
Location: India

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
09 Nov 2015, 00:41
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



Director
Joined: 17 Dec 2012
Posts: 629
Location: India

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
27 May 2017, 07:10
kilukilam wrote: All of the stock on the over counter market are designed by either 4 letter or 5 letter code that is created by using the 26 letter of the alphabet, which of the following given is the maximum number of different stock that can be designed with these code
a. 2 (26)^5 b. 26(26)^4 c. 27(26)^4 d. 26(26)^5 e. 27(26)^5 1. The maximum is when alphabets are repeating and ordering is important, which is n^r 2. For 4 letter codes it is 26^4 3. for 5 letter codes it is 26^5 4. Total is (26^4 + 26^5)= 26^4(1+26) = 27(26)^4
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



Intern
Joined: 30 May 2017
Posts: 11

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
31 May 2017, 11:23
amit2k9 wrote: 26^4 + 26^5
26^4(26+1)
C Can someone explain the step where we get (26 + 1). I follow up until that point. Unsure how we get that part.



Math Expert
Joined: 02 Sep 2009
Posts: 50002

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
31 May 2017, 12:27



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
05 Jun 2017, 16:11
kilukilam wrote: All of the stock on the over counter market are designed by either 4 letter or 5 letter code that is created by using the 26 letter of the alphabet, which of the following given is the maximum number of different stock that can be designed with these code
a. 2 (26)^5 b. 26(26)^4 c. 27(26)^4 d. 26(26)^5 e. 27(26)^5 We need to determine the maximum number of different stocks that can be designated by a 4letter or 5letter code that is created by using the 26 letters of the alphabet. Number of 5letter codes: 26 x 26 x 26 x 26 x 26 = 26^5 Number of 4letter codes: 26 x 26 x 26 x 26 = 26^4 Since the stocks can be designated by a 4letter OR 5letter code, we must add our results together to determine the maximum number of codes that can be created. 26^5 + 26^4 = 26^4(26 + 1) = 26^4(27) Answer: C
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 16 May 2017
Posts: 52
Location: India
WE: General Management (Retail Banking)

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
29 Jul 2018, 10:58
SravnaTestPrep wrote: kilukilam wrote: All of the stock on the over counter market are designed by either 4 letter or 5 letter code that is created by using the 26 letter of the alphabet, which of the following given is the maximum number of different stock that can be designed with these code
a. 2 (26)^5 b. 26(26)^4 c. 27(26)^4 d. 26(26)^5 e. 27(26)^5 1. The maximum is when alphabets are repeating and ordering is important, which is n^r 2. For 4 letter codes it is 26^4 3. for 5 letter codes it is 26^5 4. Total is (26^4 + 26^5)= 26^4(1+26) = 27(26)^4 t I don't understand the logic. If alphabets are repeating then there will be many similar codes.
_________________
"The harder you work the luckier you get"



Intern
Joined: 20 Jun 2018
Posts: 31
Location: India

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
31 Jul 2018, 21:51
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 4digit code {XXXX} each digit can take 26 values (as there are 26 letters), so total # of 4digits code possible is 26^4;
The same for 5digit code {XXXXX} again each digit can take 26 values (26 letters), so total # of 5digits code possible is 26^5;
Total: \(26^4+26^5=26^4(1+26)=27*26^4\).
Answer: C. I used the 26c4 multipled 26c5 and got the answer wrong. Whats the reason for this and when should we use this formula?



Math Expert
Joined: 02 Sep 2009
Posts: 50002

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
01 Aug 2018, 00:47
Shbm 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 4digit code {XXXX} each digit can take 26 values (as there are 26 letters), so total # of 4digits code possible is 26^4;
The same for 5digit code {XXXXX} again each digit can take 26 values (26 letters), so total # of 5digits code possible is 26^5;
Total: \(26^4+26^5=26^4(1+26)=27*26^4\).
Answer: C. I used the 26c4 multipled 26c5 and got the answer wrong. Whats the reason for this and when should we use this formula? 26C4 gives the number of unordered groups of 4 different letters out of 26. For one, the order matters, {a, b, c, d} code is different from {b, a, c, d} code. Also, the letters could be repeated in the code, and 26C4 gives groups of 4 different letters. Finally, multiplying is wrong because 4letter codes and 5letter codes are different cases, so the number of possible codes should be added not multiplied. Hope it's clear.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 20 Jun 2018
Posts: 31
Location: India

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
01 Aug 2018, 22:28
Bunuel wrote: Shbm 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 4digit code {XXXX} each digit can take 26 values (as there are 26 letters), so total # of 4digits code possible is 26^4;
The same for 5digit code {XXXXX} again each digit can take 26 values (26 letters), so total # of 5digits code possible is 26^5;
Total: \(26^4+26^5=26^4(1+26)=27*26^4\).
Answer: C. I used the 26c4 multipled 26c5 and got the answer wrong. Whats the reason for this and when should we use this formula? 26C4 gives the number of unordered groups of 4 different letters out of 26. For one, the order matters, {a, b, c, d} code is different from {b, a, c, d} code. Also, the letters could be repeated in the code, and 26C4 gives groups of 4 different letters. Finally, multiplying is wrong because 4letter codes and 5letter codes are different cases, so the number of possible codes should be added not multiplied. Hope it's clear. thanks bossman. are these type of questions generally placed in the 700 level category or can be a product of the 600700 level?



Math Expert
Joined: 02 Sep 2009
Posts: 50002

Re: All of the stocks on the over the counter market are designated by eit
[#permalink]
Show Tags
01 Aug 2018, 22:44
Shbm wrote: Bunuel wrote: Shbm wrote: I used the 26c4 multipled 26c5 and got the answer wrong. Whats the reason for this and when should we use this formula? 26C4 gives the number of unordered groups of 4 different letters out of 26. For one, the order matters, {a, b, c, d} code is different from {b, a, c, d} code. Also, the letters could be repeated in the code, and 26C4 gives groups of 4 different letters. Finally, multiplying is wrong because 4letter codes and 5letter codes are different cases, so the number of possible codes should be added not multiplied. Hope it's clear. thanks bossman. are these type of questions generally placed in the 700 level category or can be a product of the 600700 level? It depends. This one for example, is 600700 level question. You can check different level combination's questions in our questions ban: https://gmatclub.com/forum/search.php?view=search_tagsHope it helps.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Re: All of the stocks on the over the counter market are designated by eit &nbs
[#permalink]
01 Aug 2018, 22:44






