Last visit was: 21 Jun 2025, 14:09 It is currently 21 Jun 2025, 14:09
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
avatar
TechWithNoExp
Joined: 06 Jun 2012
Last visit: 17 Jun 2014
Posts: 80
Own Kudos:
126
 [87]
Given Kudos: 9
Concentration: Technology, Entrepreneurship
GMAT 1: 710 Q49 V38
GMAT 1: 710 Q49 V38
Posts: 80
Kudos: 126
 [87]
4
Kudos
Add Kudos
82
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 June 2025
Posts: 102,225
Own Kudos:
Given Kudos: 93,965
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,225
Kudos: 734,310
 [24]
6
Kudos
Add Kudos
18
Bookmarks
Bookmark this Post
User avatar
EvaJager
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,267
 [9]
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,267
 [9]
6
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
General Discussion
avatar
reddevils
Joined: 12 Feb 2011
Last visit: 11 Apr 2014
Posts: 15
Own Kudos:
Given Kudos: 129
Location: India
Concentration: General Management
GMAT Date: 03-25-2014
GPA: 3.5
WE:Information Technology (Computer Software)
Posts: 15
Kudos: 5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Notice that we are not told that letters in two-letter code must be different.
Hey Bunuel,

One doubt regarding this question. Doesn't the phrase "ordered pair" mean nothing in the question? My inference was as it is an ordered pair it should be in alphabetical order.

Please clarify. Thanks.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 June 2025
Posts: 102,225
Own Kudos:
734,310
 [2]
Given Kudos: 93,965
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,225
Kudos: 734,310
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
reddevils
Hey Bunuel,

One doubt regarding this question. Doesn't the phrase "ordered pair" mean nothing in the question? My inference was as it is a ordered pair it should be in alphabetical order.

Please clarify. Thanks.

An ordered pair of letters mean that code AB considered different from code BA, so both are possible.
User avatar
m3equals333
User avatar
Retired Moderator
Joined: 20 Dec 2013
Last visit: 18 Jun 2016
Posts: 141
Own Kudos:
Given Kudos: 71
Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 720 Q49 V40
GMAT 3: 710 Q48 V40
GPA: 3.16
WE:Consulting (Finance: Venture Capital)
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I came up with 2P# + 1C# >= 60
avatar
Sumeetsar
Joined: 28 Dec 2014
Last visit: 24 May 2017
Posts: 1
Own Kudos:
1
 [1]
Given Kudos: 1
Posts: 1
Kudos: 1
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If we assume code length to be 3 i.e. ABC,AAA,AAB...SO on.. minimum number of letters required would be 4.
n^3 >=60 =>n =4

Question is framed incorrectly because it has not mentioned the code length.
If length is 2, 8 will be the answer.If length is 3 ,4 will be the answer.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 June 2025
Posts: 102,225
Own Kudos:
734,310
 [1]
Given Kudos: 93,965
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,225
Kudos: 734,310
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sumeetsar
If we assume code length to be 3 i.e. ABC,AAA,AAB...SO on.. minimum number of letters required would be 4.
n^3 >=60 =>n =4

Question is framed incorrectly because it has not mentioned the code length.
If length is 2, 8 will be the answer.If length is 3 ,4 will be the answer.

In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?

Pair means two.
User avatar
Mo2men
Joined: 26 Mar 2013
Last visit: 09 May 2023
Posts: 2,445
Own Kudos:
1,434
 [1]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Products:
Schools: Erasmus (II)
Posts: 2,445
Kudos: 1,434
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
thebogie17
In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?

A. 6
B. 7
C. 8
D. 9
E. 10


I think the official answer supplied by PR is incorrect.
I Feel that D is the correct answer, they say C.
Am I missing something?

Notice that we are not told that letters in two-letter code must be different. For example three letters A, B, and C give the following codes:
AA;
BB;
CC;
AB;
BA;
AC;
CA;
BC;
CB.

So, if we have \(n\) distinct letters, then we can make \(n^2\) different codes (since each X in XX code can take \(n\) values). As there are 60 different models of TV then \(n^2\geq{60}\) must hold true. Since \(n\) must be an integer then the least value of \(n\) is 8.

Answer: C.


Hope it helps.

Hi Bunuel,
If the prompt restricts the duplication of a letter, can I use permutation in that case? if yes, we need more than 8 so 8p2=72.

Is it correct?

Thanks
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 21 Jun 2025
Posts: 11,303
Own Kudos:
41,306
 [1]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,303
Kudos: 41,306
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Mo2men
Bunuel
thebogie17
In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?

A. 6
B. 7
C. 8
D. 9
E. 10


I think the official answer supplied by PR is incorrect.
I Feel that D is the correct answer, they say C.
Am I missing something?

Notice that we are not told that letters in two-letter code must be different. For example three letters A, B, and C give the following codes:
AA;
BB;
CC;
AB;
BA;
AC;
CA;
BC;
CB.

So, if we have \(n\) distinct letters, then we can make \(n^2\) different codes (since each X in XX code can take \(n\) values). As there are 60 different models of TV then \(n^2\geq{60}\) must hold true. Since \(n\) must be an integer then the least value of \(n\) is 8.

Answer: C.


Hope it helps.

Hi Bunuel,
If the prompt restricts the duplication of a letter, can I use permutation in that case? if yes, we need more than 8 so 8p2=72.

Is it correct?

Thanks

Hi ,
if the prompt restricts the usage
first place can be filled by n letters and 2nd place by n-1 letters..
so total ways n(n-1), which same as np2..
so you are correct....
User avatar
boynamedjoy
Joined: 29 May 2013
Last visit: 07 Dec 2022
Posts: 1
Own Kudos:
Given Kudos: 16
Location: India
Concentration: Entrepreneurship, Marketing
WE:Engineering (Telecommunications)
Posts: 1
Kudos: 6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Pls correct me,
I got 6 no of letters for 60 maximum no. of Items when the no. of letters is not mentioned for the code,


since in combination ORDER does not matter and when we place SOME digits in a different order in Permutations, ONLY one out of them is in ascending order, we can work on Combinations
say total n digits are required
single digit will be nC1...
2 digits - nC2
3 digits= nC3...and so on..
so we are looking for nC1+nC2+nC3+...nCn≥60
nC1+nC2+nC3+...nCn≥60
now,
nC0+nC1+nC2+nC3+...nCn=2^n
nC0+nC1+nC2+nC3+...nCn=2^n is a formula..

so nC1+nC2+nC3+...nCn=2^n−nC0=2^n−1
nC1+nC2+nC3+...nCn=2n−nC0=2^n−1..
so 2^n−1≥60.................2^n≥61...................so..n≥6

so n=6 will be the minimum no. of codes that can be used for arbitrary no of position in the sequential order.

pls correct if if anything wrong in the logic
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 3,003
Own Kudos:
7,861
 [2]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 3,003
Kudos: 7,861
 [2]
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
TechWithNoExp
In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?

A. 6
B. 7
C. 8
D. 9
E. 10

We can let n = the number of letters needed to make the codes. Since we can use the same letter for the second letter and the first letter, we have n choices for the first letter and n choices for the second letter also. Thus, the number of codes we can make is n x n = n^2, and we want this to be greater than or equal to 60. That is, n^2 ≥ 60.

We see that the smallest integer value of n must be 8 in order for n^2 ≥ 60; thus, the minimum number of letters that must be used is 8.

Answer: C
User avatar
Jihyo
Joined: 01 Apr 2021
Last visit: 06 Mar 2022
Posts: 55
Own Kudos:
Given Kudos: 166
Posts: 55
Kudos: 184
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello Bunuel
I thought particular order means a single order in which AB and BA both are not acceptable. So, I assumed the answer would be nC2≥60.
avatar
Aliprep
Joined: 07 Dec 2020
Last visit: 01 Jan 2025
Posts: 13
Own Kudos:
Given Kudos: 7
Products:
Posts: 13
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
thebogie17
In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?

A. 6
B. 7
C. 8
D. 9
E. 10


I think the official answer supplied by PR is incorrect.
I Feel that D is the correct answer, they say C.
Am I missing something?

Notice that we are not told that letters in two-letter code must be different. For example three letters A, B, and C give the following codes:
AA;
BB;
CC;
AB;
BA;
AC;
CA;
BC;
CB.

So, if we have \(n\) distinct letters, then we can make \(n^2\) different codes (since each X in XX code can take \(n\) values). As there are 60 different models of TV then \(n^2\geq{60}\) must hold true. Since \(n\) must be an integer then the least value of \(n\) is 8.

Answer: C.

Hope it helps.
Hi Bunuel,

Can you pls help me to understand, why are we not supposed to calculate for doubles here?
For example AB and BA are different, that's ok. We count them as 2.
But, AA and AA (or like this A1A2 and A2A1) are the same, but we are not counting for doubles and not dividing by 2!
Why is it the case here, but not in the others?
For example, there was a question with word ILLUSION, where we should calculate possibilities of different combinations from this letters and we calculated it like 8!/2!2! (because there two I's and L's).

Thank you in advance.
User avatar
Crytiocanalyst
Joined: 16 Jun 2021
Last visit: 27 May 2023
Posts: 953
Own Kudos:
Given Kudos: 309
Posts: 953
Kudos: 201
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The key to solving the above equation is getting the combination right
I guess the order is alphabhetical therefore
let us take the possiblity of 8(even though it's brute force we will get the idea of the same and afterwards we can decide )
AB,A_=>since there are seven characters that 7(6)/2= 21
B_=> since there are 6 eleminating A we have 6*5/2= 15
C_=> since there are 5 eleminating A,B we have 5*4/2=10
D_=>since there are 4 eleminating A,B,C we have 4*3/2=6
E_=>since there are 4 eleminating A,B,C ,D we have 3
Total 55
other possiblities are
FG,FH,GH, GI, HI =60
Exactly what we were looking along with alphabhetical a very tight question brute force helped may not be so useful in GMAT
Hence IMO C
User avatar
roshanoronha
Joined: 18 Dec 2022
Last visit: 31 Jul 2023
Posts: 8
Own Kudos:
Given Kudos: 61
Posts: 8
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
thebogie17
In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?

A. 6
B. 7
C. 8
D. 9
E. 10


I think the official answer supplied by PR is incorrect.
I Feel that D is the correct answer, they say C.
Am I missing something?

Notice that we are not told that letters in two-letter code must be different. For example three letters A, B, and C give the following codes:
AA;
BB;
CC;
AB;
BA;
AC;
CA;
BC;
CB.

So, if we have \(n\) distinct letters, then we can make \(n^2\) different codes (since each X in XX code can take \(n\) values). As there are 60 different models of TV then \(n^2\geq{60}\) must hold true. Since \(n\) must be an integer then the least value of \(n\) is 8.

Answer: C.

Similar questions to practice:
https://gmatclub.com/forum/if-a-code-wo ... 26652.html
https://gmatclub.com/forum/all-of-the-s ... 26630.html
https://gmatclub.com/forum/the-simplast ... 05845.html
https://gmatclub.com/forum/a-4-letter-c ... 59065.html
https://gmatclub.com/forum/a-certain-st ... 86656.html
https://gmatclub.com/forum/a-5-digit-co ... 32263.html
https://gmatclub.com/forum/a-company-th ... 95946.html

Hope it helps.

Hi Bunuel,

Please help me understand this. If not explicitly mentioned in the question, do we consider repetition allowed or not? I am really confused.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,243
Own Kudos:
Posts: 37,243
Kudos: 1,002
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
102225 posts
PS Forum Moderator
653 posts