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The telephone company wants to add an area code composed of

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The telephone company wants to add an area code composed of  [#permalink]

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New post Updated on: 25 Oct 2013, 07:37
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The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

(A) 246
(B) 248
(C) 492
(D) 15,128
(E) 30,256

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Originally posted by Macedon on 20 Sep 2005, 10:20.
Last edited by Bunuel on 25 Oct 2013, 07:37, edited 1 time in total.
Edited the question and added the OA.
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 25 Oct 2013, 07:41
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Macedon wrote:
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

(A) 246
(B) 248
(C) 492
(D) 15,128
(E) 30,256


# of 2-letter codes possible from 124 different signs = 124*124.
# of 2-letter codes possible from 122 different signs = 122*122.

The difference = 124^2 - 122^2 = (124 - 122)(124 + 122) = 492.

Answer: C.

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New post 20 Sep 2005, 10:58
yep, agree with Ranga41

124^2-122^2

We had this question about a week ago.

http://www.gmatclub.com/phpbb/viewtopic.php?t=20091
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 25 Oct 2013, 05:22
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Macedon wrote:
35. The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

a) 246
b) 248
c) 492
d) 15,128
e) 30,256

Is there some bit missing in the text?


OK let's take a crack at this one.
So basically we have 144^2 - 142^2
So then (144+142)(144-142)
(246)(2) = 492

Hope it helps
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 26 Oct 2013, 01:39
Bunuel wrote:
Macedon wrote:
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

(A) 246
(B) 248
(C) 492
(D) 15,128
(E) 30,256


# of 2-letter codes possible from 124 different signs = 124*124.
# of 2-letter codes possible from 122 different signs = 122*122.

The difference = 124^2 - 122^2 = (124 - 122)(124 + 122) = 492.

Answer: C.

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Hope this helps.

Hi,

I tried to calculate this via taking the 22 left characters and making 22^2 but did not get the right result.
What is flawed with the reasoning?
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 26 Oct 2013, 03:36
ronr34 wrote:
Bunuel wrote:
Macedon wrote:
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

(A) 246
(B) 248
(C) 492
(D) 15,128
(E) 30,256


# of 2-letter codes possible from 124 different signs = 124*124.
# of 2-letter codes possible from 122 different signs = 122*122.

The difference = 124^2 - 122^2 = (124 - 122)(124 + 122) = 492.

Answer: C.

Similar questions to practice:
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a-4-letter-code-word-consists-of-letters-a-b-and-c-if-the-59065.html
a-5-digit-code-consists-of-one-number-digit-chosen-from-132263.html
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Hope this helps.

Hi,

I tried to calculate this via taking the 22 left characters and making 22^2 but did not get the right result.
What is flawed with the reasoning?


There are 2 left letters not 22.
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 27 Oct 2013, 06:32
I have solved in different way:-

The first place can be filled in two ways (remaining 2 special character) and the second place can be filled by any of 122 characters

2 x 122 = 244

Again the first place can be filled up by 122 characters and the next place can be filled up by 2 characters

122 x 2 = 244

Finally the two places could be filled in 2 x 2 =4 ways.

Adding the above 3 cases 244 + 244 + 4 = 492 ways.
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 21 Feb 2015, 21:20
I started this question by looking at 124C2 - 122C2 ... could someone please tell me why this is the incorrect way of handling this question?

Combinatorics is for unordered sets... this is unordered?

Any help would be much appreciated. Thanks.
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 22 Feb 2015, 00:06
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Hi icetray,

This question essentially discusses "lengthening" phone numbers. In a phone number, the order of the numbers DOES matter, so when adding two more 'characters' to the phone number, the order of those two characters would also matter. Thus, we're dealing with a permutation and not a combination.

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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 22 Feb 2015, 09:44
EMPOWERgmatRichC wrote:
Hi icetray,

This question essentially discusses "lengthening" phone numbers. In a phone number, the order of the numbers DOES matter, so when adding two more 'characters' to the phone number, the order of those two characters would also matter. Thus, we're dealing with a permutation and not a combination.

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Thank You Rich for the explanation. Do have you any suggestions on questions/materials within this forum that I can practice deciding whether or not a set of data is ordered or unordered? Thank You.
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 22 Feb 2015, 14:03
Hi icetray,

The forums on this site likely have anything GMAT-related that you might be looking for. Before you put too much time into Permutations and Combinations though, we should probably look at how you're performing on the OVERALL GMAT.

Permutations and Combinations are relatively rare subjects on the actual Test; while you're likely to see at least 1 of each on Test Day, you won't see more than maybe 2 or 3 of either (at the high end). There are MANY different subjects that show up more often: Algebra, Arithmetic, Geometry, Formulas, ratios, etc. (and the broad category of DS, which includes all of the previous categories). Every major Verbal category (SC, RC and CR) will also show up more often than Permutations or Combinations.

To gauge what you should be focusing on, I need to know a bit more about your practice CAT scores and your work so far:

1) How have you been scoring on your CATs (including the Quant and Verbal Scaled Scores)?
2) What materials have you been using so far?
3) What is your goal score?
4) When are you planning to take the GMAT?

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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 21 Sep 2017, 14:55
Macedon wrote:
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

(A) 246
(B) 248
(C) 492
(D) 15,128
(E) 30,256


The 124 different signs can generate a total of 124 x 124 different 2-letter area codes. The 122 different signs can generate a total of 122 x 122 different 2-letter area codes. The difference between using 124 signs and 122 signs is:

124^2 - 122^2 = (124 - 122)(124 + 122) = 2 x 246 = 492

Answer: C
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 17 Feb 2018, 00:45
I got this completely wrong. I used combinations and did 124C2- 122C2. Would I ever be able to get the answer with this method.Can someone help pls.
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Re: The telephone company wants to add an area code composed of  [#permalink]

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New post 17 Feb 2018, 03:44
Total Number of 2 letter codes possible=124^2
Number of codes formed using 122 letters=122^2
So required answer=124^2-122^2=(124+122)(124-122)=246*2=492
So answer is C
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The telephone company wants to add an area code composed of  [#permalink]

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New post 23 Jul 2019, 08:21
Macedon wrote:
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

(A) 246
(B) 248
(C) 492
(D) 15,128
(E) 30,256


Total codes to be made out of 124 signs = 124*124 (each letter can be chosen in 124 ways as repetition is allowed)

Total codes to be made out of 122 signs = 122*122 (each letter can be chosen in 124 ways as repetition is allowed)

Additional codes to be created \(= 124^2 - 122^2 = (124+122)*(124-122) = 246*2 = 492\)

Answer: Option C


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