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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In a certain appliance store, each model of television is [#permalink]
31 Jul 2012, 12:15

1

This post received KUDOS

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

54% (02:16) correct
46% (01:46) wrong based on 180 sessions

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?

In a certain appliance store, each model of television is [#permalink]
31 Jul 2012, 12:37

2

This post received KUDOS

1

This post was BOOKMARKED

thebogie17 wrote:

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?

If n is the number of distinct letters used to create the two lettered codes, then a total of \(n * n = n^2\) different codes can be created. We need \(n^2\geq60\). The smallest n which fulfills this condition is n = 8.

Answer C _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Last edited by EvaJager on 30 Jul 2014, 05:52, edited 2 times in total.

Re: In a certain appliance store, each model of television is [#permalink]
31 Jul 2012, 12:54

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

thebogie17 wrote:

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.

Re: In a certain appliance store, each model of television is [#permalink]
20 Dec 2013, 02:36

Bunuel wrote:

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.

Last edited by reddevils on 20 Dec 2013, 02:40, edited 1 time in total.

Re: In a certain appliance store, each model of television is [#permalink]
20 Dec 2013, 02:39

2

This post received KUDOS

Expert's post

reddevils wrote:

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. _________________

Re: In a certain appliance store, each model of television is [#permalink]
12 Jun 2015, 00:49

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. _________________

In a certain appliance store, each model of television is [#permalink]
28 Jun 2015, 13:48

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.

Re: In a certain appliance store, each model of television is [#permalink]
28 Jun 2015, 23:34

Expert's post

Sumeetsar wrote:

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?

Re: In a certain appliance store, each model of television is [#permalink]
30 Jun 2015, 05:08

Bunuel wrote:

thebogie17 wrote:

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.

Re: In a certain appliance store, each model of television is [#permalink]
30 Jun 2015, 05:31

1

This post received KUDOS

Mo2men wrote:

Bunuel wrote:

thebogie17 wrote:

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....

gmatclubot

Re: In a certain appliance store, each model of television is
[#permalink]
30 Jun 2015, 05:31

Interested in applying for an MBA? In the fourth and final part of our live QA series with guest expert Chioma Isiadinso, co-founder of consultancy Expartus and former admissions...