Author 
Message 
TAGS:

Hide Tags

Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 73
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)

Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
01 May 2013, 09:47
Question Stats:
74% (01:44) correct 26% (02:27) wrong based on 594 sessions
HideShow timer Statistics
Each student at a certain university is given a fourcharacter identification code, the
rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules? A. 135,200 B. 67,600 C. 64,000 D. 60,840 E. 58,500
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 60647

Re: Each student at a certain university is given a fourchar
[#permalink]
Show Tags
30 Sep 2013, 00:41




Intern
Joined: 14 Feb 2013
Posts: 28

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
01 May 2013, 10:01
manishuol wrote: Each student at a certain university is given a fourcharacter identification code, the
rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?
A . 135,200 B. 67,600 C. 64,000 D. 60,840 E. 58,500 Four character identification code _ _ _ _ First two parts for the code, are digits between 09, therefore, 10 options for the first part of the code, and as characters may be repeated, 10 options for the second part as well Therefore, we have 10 X 10 possibilities for the first and second part of the code Last two parts of the code, are characters selected from the 26 letters of the alphabet, therefore, 26 options for the third part of the code, and as characters may be repeated, 26 options for the fourth part as well Therefore, we have 26 X 26 possibilities for the third and fourth part of the code so, in all total no. of different identification codes generated following these rules = 10 X 10 X 26 X 26 = 67600 Answer B




Current Student
Status: Chasing my MBB Dream!
Joined: 29 Aug 2012
Posts: 1095
Location: United States (DC)
WE: General Management (Aerospace and Defense)

Each student at a certain university is given a fourchar
[#permalink]
Show Tags
30 Sep 2013, 00:36
Source : Jeff Sackmann Extreme Challenge Each student at a certain university is given a fourcharacter identification code, the
rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules? (A) 135,200 (B) 67,600 (C) 64,000 (D) 60,840 (E) 58,500
_________________



Manager
Joined: 15 Aug 2013
Posts: 226

Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
23 Aug 2014, 10:37
karishmatandon wrote: manishuol wrote: Each student at a certain university is given a fourcharacter identification code, the
rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?
A . 135,200 B. 67,600 C. 64,000 D. 60,840 E. 58,500 Four character identification code _ _ _ _ First two parts for the code, are digits between 09, therefore, 10 options for the first part of the code, and as characters may be repeated, 10 options for the second part as well Therefore, we have 10 X 10 possibilities for the first and second part of the code Last two parts of the code, are characters selected from the 26 letters of the alphabet, therefore, 26 options for the third part of the code, and as characters may be repeated, 26 options for the fourth part as well Therefore, we have 26 X 26 possibilities for the third and fourth part of the code so, in all total no. of different identification codes generated following these rules = 10 X 10 X 26 X 26 = 67600 Answer B Can't it be Letter.Number.Letter.Number? Doesn't this add further combinations? Additional question  I followed the approach of 26C2 * 10C2. Why is that wrong? Is it because the combination formula take's the order into account? How would I unorder it?



Intern
Joined: 13 May 2014
Posts: 19
GMAT Date: 11012014

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
25 May 2015, 07:37
Can someone help me out with this question..



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3230

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
26 May 2015, 04:57
sagarag wrote: Can someone help me out with this question.. Hi sagarag, The question here is asking us to fill four places with given set of letters and digits. We are given a constraint that first two places can only be filled with digits and the last two places can only be filled with letters. We are also told that the characters can be repeated. Let's see the number of ways in which each place can be filled. 1st Place: The 1st place of the code needs to be filled with digits only. The total number of digits which we have is 10 ( from 0 to 9 both inclusive). So, there are 10 ways in which we can fill the first place. 2nd Place: The 2nd place also needs to be filled with digits only. Since we are given that digits can be repeated, we have again 10 ways (from 0 to 9 both inclusive) to fill the 2nd place. Had the question constrained us that digits can't be repeated, we would have had 9 ways to fill the 2nd place( as one of the digits would have been used to fill the 1st place) 3rd place: The 3rd place can be filled with letters only. The total number of letters which we have is 26 (from A to Z both inclusive). So there are 26 ways in which we can fill the 3rd place. 4th place: The 4th place also needs to be filled with letters. Since the letters can be repeated, we have again 26 ways (from A to Z both inclusive) to fill the 4th place. Had the question constrained us that letters can't be repeated, we would have had 25 ways to fill the 4th place( as one of the letters would have been used to fill the 3rd place). As the code constitutes of four characters, the number of ways of filling the four places can be written as = 10 * 10 * 26 * 26 = 67,600 ways. Hope it's clear. Let me know if you have trouble at any point of this solution Regards Harsh
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15975
Location: United States (CA)

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
26 May 2015, 10:32
Hi All Although the question is from last year, it doesn't look like anyone answered russ9's question. There are a couple of reasons why using the Combination Formula (as he did) is incorrect: 1) We're dealing with unique codes, so order matters (the prompt states "...the same characters used in a different order constitute a different code..." Thus, permutation "math" is appropriate here. 2) Duplicate characters ARE allowed, so choosing one character does NOT impact how we choose the next. When trying to decide whether to use Combination "math" or Permutation "math", it's usually best to do a quick 'sketch' of what you're after. If ABC is different from BAC and CBA, then it's a permutation. If a GROUP of letters (A, B and C) is the same group as (B, A and C), then it's a combination. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 20 Oct 2015
Posts: 7
Concentration: Nonprofit, Entrepreneurship
GPA: 2.67
WE: Engineering (Manufacturing)

Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
14 Dec 2015, 09:17
karishmatandon wrote: manishuol wrote: Each student at a certain university is given a fourcharacter identification code, the
rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?
A . 135,200 B. 67,600 C. 64,000 D. 60,840 E. 58,500 Four character identification code _ _ _ _ First two parts for the code, are digits between 09, therefore, 10 options for the first part of the code, and as characters may be repeated, 10 options for the second part as well Therefore, we have 10 X 10 possibilities for the first and second part of the code Last two parts of the code, are characters selected from the 26 letters of the alphabet, therefore, 26 options for the third part of the code, and as characters may be repeated, 26 options for the fourth part as well Therefore, we have 26 X 26 possibilities for the third and fourth part of the code so, in all total no. of different identification codes generated following these rules = 10 X 10 X 26 X 26 = 67600 Answer B Great explanation of the governing concept. I'd like to add something, though. Since time is a concern I found myself using this shortcut: Instead of 10 x 10 x 26 x 26 I used 10 x 10 x 26 x 25. Changing the last 26 to a 25 allowed me to multiply by 100 then divide by 4 (=25) instead of multiplying by another 26. 10 x 10 x 26 x 100 / 4 10 x 10 x 26 = 2600, 2600 x 100 = 260.000, 260.000 / 4 = 65.000 You know that 26 is barely above 25, so you're looking for the answer that is above, but close to 65.000. 67.600 is the clear answer. Saved myself a good 2030 seconds because I could do the whole calc in my head. Another look at it shows me a quicker way, as soon as you know that its 10 x 10 x 26 x 26 you know that the answer's last nonzero digit will be a 6 (you're first nonzero calculation in long multiplication will be 6 x 6 [= 36]). There's only one choice! Just my $0.02 .



Intern
Joined: 16 Dec 2013
Posts: 32
Location: United States
GPA: 3.7

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
14 Dec 2015, 15:52
Bunuel...Why are we not multiplying it by 4! to account for the different ordering that can be got. Bunuel wrote:



Manager
Joined: 27 Aug 2014
Posts: 53
Location: Canada
Concentration: Strategy, Technology
GPA: 3.66
WE: Consulting (Consulting)

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
26 Jan 2017, 21:49
Numbers and alphabets can repeat.
so 10*10*26*26.
Only option B has a 6 followed by two zeroes.



Manager
Joined: 07 May 2015
Posts: 68

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
23 Feb 2017, 03:03
EgmatQuantExpert wrote: sagarag wrote: Can someone help me out with this question.. Hi sagarag, The question here is asking us to fill four places with given set of letters and digits. We are given a constraint that first two places can only be filled with digits and the last two places can only be filled with letters. We are also told that the characters can be repeated. Let's see the number of ways in which each place can be filled. 1st Place: The 1st place of the code needs to be filled with digits only. The total number of digits which we have is 10 ( from 0 to 9 both inclusive). So, there are 10 ways in which we can fill the first place. 2nd Place: The 2nd place also needs to be filled with digits only. Since we are given that digits can be repeated, we have again 10 ways (from 0 to 9 both inclusive) to fill the 2nd place. Had the question constrained us that digits can't be repeated, we would have had 9 ways to fill the 2nd place( as one of the digits would have been used to fill the 1st place) 3rd place: The 3rd place can be filled with letters only. The total number of letters which we have is 26 (from A to Z both inclusive). So there are 26 ways in which we can fill the 3rd place. 4th place: The 4th place also needs to be filled with letters. Since the letters can be repeated, we have again 26 ways (from A to Z both inclusive) to fill the 4th place. Had the question constrained us that letters can't be repeated, we would have had 25 ways to fill the 4th place( as one of the letters would have been used to fill the 3rd place). As the code constitutes of four characters, the number of ways of filling the four places can be written as = 10 * 10 * 26 * 26 = 67,600 ways. Hope it's clear. Let me know if you have trouble at any point of this solution Regards Harsh Do we need to worry about numbers repeating and coming up with duplicate combination? thanks in advance!



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9142
Location: United States (CA)

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
27 Feb 2017, 11:54
manishuol wrote: Each student at a certain university is given a fourcharacter identification code, the
rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?
A. 135,200 B. 67,600 C. 64,000 D. 60,840 E. 58,500 We need to create a 4digit code in which the first two characters are digits between 0 and 9 inclusive and the last two are selected from the 26 letters of the alphabet. Since characters can be repeated, we have: Character 1 = 10 options Character 2 = 10 options Character 3 = 26 options Character 4 = 26 options Thus, the codes can be created in 10 x 10 x 26 x 26 = 67,600 ways. Answer: B
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 870
GMAT 1: 790 Q51 V49

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
27 Feb 2017, 12:42
neeraj609 wrote: EgmatQuantExpert wrote: sagarag wrote: Can someone help me out with this question.. Hi sagarag, The question here is asking us to fill four places with given set of letters and digits. We are given a constraint that first two places can only be filled with digits and the last two places can only be filled with letters. We are also told that the characters can be repeated. Let's see the number of ways in which each place can be filled. 1st Place: The 1st place of the code needs to be filled with digits only. The total number of digits which we have is 10 ( from 0 to 9 both inclusive). So, there are 10 ways in which we can fill the first place. 2nd Place: The 2nd place also needs to be filled with digits only. Since we are given that digits can be repeated, we have again 10 ways (from 0 to 9 both inclusive) to fill the 2nd place. Had the question constrained us that digits can't be repeated, we would have had 9 ways to fill the 2nd place( as one of the digits would have been used to fill the 1st place) 3rd place: The 3rd place can be filled with letters only. The total number of letters which we have is 26 (from A to Z both inclusive). So there are 26 ways in which we can fill the 3rd place. 4th place: The 4th place also needs to be filled with letters. Since the letters can be repeated, we have again 26 ways (from A to Z both inclusive) to fill the 4th place. Had the question constrained us that letters can't be repeated, we would have had 25 ways to fill the 4th place( as one of the letters would have been used to fill the 3rd place). As the code constitutes of four characters, the number of ways of filling the four places can be written as = 10 * 10 * 26 * 26 = 67,600 ways. Hope it's clear. Let me know if you have trouble at any point of this solution Regards Harsh Do we need to worry about numbers repeating and coming up with duplicate combination? thanks in advance! That's a great question. In this problem, you don't need to worry about that. Here's why. Imagine that instead of what it says in the problem, you had just a twodigit code, and both digits had to be 1, 2, or 3. (I'm just doing this so that we get a comparable example that's smaller and easier to talk about.) As in the problem, digits can be repeated, and the same digits in a different order are different codes. You'd multiply 3*3, and that wouldn't result in counting any cases twice. There are 9 possibilities. The reason that works, is because when you multiply 3*3, you're doing something similar to 'counting paths'. There are three possible 'paths' at the very beginning: 1 2 3 Then, for each of these paths, there are three more paths when you're choosing the second digit: 1  1 1  2 1  3 2  1 2  2 2  3 3  1 3  2 3  3 Notice that only one of those paths gives you, for instance, '11' as a code. That's how you know you haven't counted '11' twice (even though it has two of the same digit).
_________________



Manager
Joined: 20 Aug 2015
Posts: 89
Location: India
GPA: 3

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
02 Sep 2017, 11:52
Avinashs87 wrote: Bunuel...Why are we not multiplying it by 4! to account for the different ordering that can be got.
To anyone wondering why, multiplying by 4! means getting different orders like Number.Number.Alphabet.Alphabet and Number.Alphabet.Number.Alphabet which is not required here.



Intern
Joined: 21 Jun 2015
Posts: 43
Location: India
Concentration: Finance, General Management
GPA: 3.32
WE: Programming (Computer Software)

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
22 Sep 2017, 00:11
in all total no. of different identification codes generated following these rules = 10 X 10 X 26 X 26 = 67600
Answer B



NonHuman User
Joined: 09 Sep 2013
Posts: 14017

Re: Each student at a certain university is given a fourcharact
[#permalink]
Show Tags
10 Dec 2019, 12:34
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.
_________________




Re: Each student at a certain university is given a fourcharact
[#permalink]
10 Dec 2019, 12:34






