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.
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]
Show Tags
31 Jul 2012, 13:15
1
13
00:00
A
B
C
D
E
Difficulty:
75% (hard)
Question Stats:
50% (01:39) correct 50% (02:04) wrong based on 395 sessions
HideShow timer Statistics
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?
Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
31 Jul 2012, 13:54
3
8
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.
In a certain appliance store, each model of television is
[#permalink]
Show Tags
Updated on: 30 Jul 2014, 06:52
3
3
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.
Originally posted by EvaJager on 31 Jul 2012, 13:37.
Last edited by EvaJager on 30 Jul 2014, 06:52, edited 2 times in total.
Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
Updated on: 20 Dec 2013, 03:40
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.
Originally posted by reddevils on 20 Dec 2013, 03:36.
Last edited by reddevils on 20 Dec 2013, 03:40, edited 1 time in total.
Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
20 Dec 2013, 03:39
2
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.
_________________
In a certain appliance store, each model of television is
[#permalink]
Show Tags
28 Jun 2015, 14:48
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]
Show Tags
29 Jun 2015, 00:34
1
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]
Show Tags
30 Jun 2015, 06:08
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]
Show Tags
30 Jun 2015, 06:31
1
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....
_________________
Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
19 Jul 2017, 23:20
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.
Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
25 Jul 2017, 11:13
1
TechWithNoExp 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
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
_________________
Jeffery Miller Head of GMAT Instruction
GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions
Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
29 Jul 2018, 23:24
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.
_________________
close
50% (01:39) correct 
