In a certain appliance store, each model of television is : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 06:16

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In a certain appliance store, each model of television is

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Jun 2012
Posts: 82
Concentration: Technology, Entrepreneurship
GMAT 1: 710 Q49 V38
Followers: 3

Kudos [?]: 26 [1] , given: 9

In a certain appliance store, each model of television is [#permalink]

### Show Tags

31 Jul 2012, 12:15
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:08) correct 45% (01:37) wrong based on 269 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?
[Reveal] Spoiler: OA

_________________

Try to make my way to San Jose.

??? class of 2016

Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 100

Kudos [?]: 892 [3] , given: 43

In a certain appliance store, each model of television is [#permalink]

### Show Tags

31 Jul 2012, 12:37
3
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.

_________________

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.
Math Expert
Joined: 02 Sep 2009
Posts: 36597
Followers: 7093

Kudos [?]: 93429 [1] , given: 10563

Re: In a certain appliance store, each model of television is [#permalink]

### Show Tags

31 Jul 2012, 12:54
1
KUDOS
Expert's post
3
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.

Similar questions to practice:
if-a-code-word-is-defined-to-be-a-sequence-of-different-126652.html
all-of-the-stocks-on-the-over-the-counter-market-are-126630.html
the-simplastic-language-has-only-2-unique-values-and-105845.html
a-4-letter-code-word-consists-of-letters-a-b-and-c-if-the-59065.html
a-certain-stock-exchange-designates-each-stock-with-a-86656.html
a-5-digit-code-consists-of-one-number-digit-chosen-from-132263.html
a-company-that-ships-boxes-to-a-total-of-12-distribution-95946.html

Hope it helps.
_________________
Intern
Joined: 12 Feb 2011
Posts: 17
Location: India
Concentration: General Management
GMAT Date: 03-25-2014
GPA: 3.5
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 5 [0], given: 129

Re: In a certain appliance store, each model of television is [#permalink]

### Show Tags

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.

Last edited by reddevils on 20 Dec 2013, 02:40, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 36597
Followers: 7093

Kudos [?]: 93429 [2] , given: 10563

Re: In a certain appliance store, each model of television is [#permalink]

### Show Tags

20 Dec 2013, 02:39
2
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.

An ordered pair of letters mean that code AB considered different from code BA, so both are possible.
_________________
Moderator
Joined: 20 Dec 2013
Posts: 189
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)
Followers: 7

Kudos [?]: 66 [0], given: 71

Re: In a certain appliance store, each model of television is [#permalink]

### Show Tags

14 Jan 2014, 21:57
I came up with 2P# + 1C# >= 60
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13499
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: In a certain appliance store, each model of television is [#permalink]

### Show Tags

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.
_________________
Intern
Joined: 28 Dec 2014
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 1

In a certain appliance store, each model of television is [#permalink]

### Show Tags

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.
Math Expert
Joined: 02 Sep 2009
Posts: 36597
Followers: 7093

Kudos [?]: 93429 [1] , given: 10563

Re: In a certain appliance store, each model of television is [#permalink]

### Show Tags

28 Jun 2015, 23:34
1
KUDOS
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?

Pair means two.
_________________
Director
Joined: 26 Mar 2013
Posts: 674
Followers: 3

Kudos [?]: 133 [0], given: 96

Re: In a certain appliance store, each model of television is [#permalink]

### Show Tags

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.

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
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4240
Followers: 329

Kudos [?]: 3464 [1] , given: 101

Re: In a certain appliance store, each model of television is [#permalink]

### Show Tags

30 Jun 2015, 05:31
1
KUDOS
Expert's post
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.

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....
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13499
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: In a certain appliance store, each model of television is [#permalink]

### Show Tags

02 Jul 2016, 19:32
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: In a certain appliance store, each model of television is   [#permalink] 02 Jul 2016, 19:32
Similar topics Replies Last post
Similar
Topics:
A couple who own an appliance store discover that if they advertise a 5 02 Feb 2016, 01:00
A television manufacturer produces 600 units of a certain model each m 1 21 Dec 2015, 19:53
7 Craig sells major appliances. For each appliance he sells, C 9 22 Jan 2014, 01:19
31 Stores X, Y, and Z each sell a certain item that has a given 10 14 Oct 2013, 05:24
In a certain candy store in New York, each orange candy cost 2 31 Oct 2010, 06:20
Display posts from previous: Sort by