Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 06 Jun 2012
Posts: 82
Concentration: Technology, Entrepreneurship

In a certain appliance store, each model of television is
[#permalink]
Show Tags
31 Jul 2012, 13:15
Question Stats:
51% (01:18) correct 49% (01:43) wrong based on 379 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?
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Try to make my way to San Jose.
??? class of 2016




Math Expert
Joined: 02 Sep 2009
Posts: 48110

Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
31 Jul 2012, 13:54
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 twoletter 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: ifacodewordisdefinedtobeasequenceofdifferent126652.htmlallofthestocksontheoverthecountermarketare126630.htmlthesimplasticlanguagehasonly2uniquevaluesand105845.htmla4lettercodewordconsistsoflettersabandcifthe59065.htmlacertainstockexchangedesignateseachstockwitha86656.htmla5digitcodeconsistsofonenumberdigitchosenfrom132263.htmlacompanythatshipsboxestoatotalof12distribution95946.htmlHope 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




Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

In a certain appliance store, each model of television is
[#permalink]
Show Tags
Updated on: 30 Jul 2014, 06:52
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.




Intern
Joined: 12 Feb 2011
Posts: 16
Location: India
Concentration: General Management
GMAT Date: 03252014
GPA: 3.5
WE: Information Technology (Computer Software)

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 twoletter 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.



Math Expert
Joined: 02 Sep 2009
Posts: 48110

Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
20 Dec 2013, 03:39



Retired Moderator
Joined: 20 Dec 2013
Posts: 180
Location: United States (NY)
GMAT 1: 640 Q44 V34 GMAT 2: 710 Q48 V40 GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)

Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
14 Jan 2014, 22:57
I came up with 2P# + 1C# >= 60
_________________
MY GMAT BLOG  ADVICE  OPINIONS  ANALYSIS



Intern
Joined: 28 Dec 2014
Posts: 1

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.



Math Expert
Joined: 02 Sep 2009
Posts: 48110

Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
29 Jun 2015, 00:34



SVP
Joined: 26 Mar 2013
Posts: 1785

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 twoletter 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



Math Expert
Joined: 02 Aug 2009
Posts: 6561

Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
30 Jun 2015, 06:31
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 twoletter 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 n1 letters.. so total ways n(n1), which same as np2.. so you are correct....
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 29 May 2013
Posts: 1
Location: India
Concentration: Entrepreneurship, Marketing
WE: Engineering (Telecommunications)

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.
pls correct if if anything wrong in the logic



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2781

Re: In a certain appliance store, each model of television is
[#permalink]
Show Tags
25 Jul 2017, 11:13
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 SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 7778

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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In a certain appliance store, each model of television is &nbs
[#permalink]
29 Jul 2018, 23:24






