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

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Kudos [?]: 17 [1] , given: 9

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

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Kudos [?]: 591 [2] , given: 43

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

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Last edited by EvaJager on 30 Jul 2014, 05:52, edited 2 times in total.
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Kudos [?]: 41046 [1] , given: 5661

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

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Hope it helps.
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Kudos [?]: 5 [0], given: 129

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.

Last edited by reddevils on 20 Dec 2013, 02:40, edited 1 time in total.
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Kudos [?]: 41046 [2] , given: 5661

Re: In a certain appliance store, each model of television is [#permalink]  20 Dec 2013, 02:39
2
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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.
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Kudos [?]: 41 [0], given: 71

Re: In a certain appliance store, each model of television is [#permalink]  14 Jan 2014, 21:57
Expert's post
I came up with 2P# + 1C# >= 60
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Re: In a certain appliance store, each model of television is   [#permalink] 14 Jan 2014, 21:57
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# In a certain appliance store, each model of television is

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