GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 Jan 2020, 20:37 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In a certain appliance store, each model of television is

Author Message
TAGS:

### Hide Tags

Manager  Joined: 06 Jun 2012
Posts: 80
Concentration: Technology, Entrepreneurship
GMAT 1: 710 Q49 V38
In a certain appliance store, each model of television is  [#permalink]

### Show Tags

2
22 00:00

Difficulty:   75% (hard)

Question Stats: 50% (01:35) correct 50% (02:04) wrong based on 446 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?
Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: In a certain appliance store, each model of television is  [#permalink]

### Show Tags

5
9
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.
_________________
Director  Joined: 22 Mar 2011
Posts: 583
WE: Science (Education)
In a certain appliance store, each model of television is  [#permalink]

### Show Tags

4
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.

_________________
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.
##### General Discussion
Intern  Joined: 12 Feb 2011
Posts: 16
Location: India
Concentration: General Management
GMAT Date: 03-25-2014
GPA: 3.5
WE: Information Technology (Computer Software)
Re: In a certain appliance store, each model of television is  [#permalink]

### Show Tags

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.

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 V
Joined: 02 Sep 2009
Posts: 60647
Re: In a certain appliance store, each model of television is  [#permalink]

### Show Tags

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.

An ordered pair of letters mean that code AB considered different from code BA, so both are possible.
_________________
Retired Moderator Joined: 20 Dec 2013
Posts: 166
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

I came up with 2P# + 1C# >= 60
_________________
Intern  B
Joined: 28 Dec 2014
Posts: 1
In a certain appliance store, each model of television is  [#permalink]

### Show Tags

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 V
Joined: 02 Sep 2009
Posts: 60647
Re: In a certain appliance store, each model of television is  [#permalink]

### Show Tags

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?

Pair means two.
_________________
SVP  V
Joined: 26 Mar 2013
Posts: 2344
Concentration: Operations, Strategy
Schools: Erasmus '21 (M\$)
Re: In a certain appliance store, each model of television is  [#permalink]

### Show Tags

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
Math Expert V
Joined: 02 Aug 2009
Posts: 8336
Re: In a certain appliance store, each model of television is  [#permalink]

### Show Tags

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.

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....
_________________
Intern  B
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

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 G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806
Re: In a certain appliance store, each model of television is  [#permalink]

### Show Tags

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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 14017
Re: In a certain appliance store, each model of television is  [#permalink]

### Show Tags

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] 14 Sep 2019, 03:45
Display posts from previous: Sort by

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