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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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20 Sep 2005, 09:20
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Oct 2013, 06:37, edited 1 time in total.
Edited the question and added the OA.
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20 Sep 2005, 09:58
yep, agree with Ranga41

124^2-122^2

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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25 Oct 2013, 04:22
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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
Cheers!
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Re: The telephone company wants to add an area code composed of [#permalink]

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25 Oct 2013, 06:41
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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.

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

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26 Oct 2013, 00:39
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.

Similar questions to practice:
each-student-at-a-certain-university-is-given-a-four-charact-151945.html
all-of-the-stocks-on-the-over-the-counter-market-are-126630.html
if-a-code-word-is-defined-to-be-a-sequence-of-different-126652.html
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
a-company-that-ships-boxes-to-a-total-of-12-distribution-95946.html
a-company-plans-to-assign-identification-numbers-to-its-empl-69248.html
the-security-gate-at-a-storage-facility-requires-a-five-109932.html
all-of-the-bonds-on-a-certain-exchange-are-designated-by-a-150820.html
a-local-bank-that-has-15-branches-uses-a-two-digit-code-to-98109.html
a-researcher-plans-to-identify-each-participant-in-a-certain-134584.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?
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Re: The telephone company wants to add an area code composed of [#permalink]

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26 Oct 2013, 02:36
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.

Similar questions to practice:
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m04q29-color-coding-70074.html

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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26 Oct 2013, 08:01
Bunuel wrote:

There are 2 left letters not 22.

So how do you get the answer?
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Re: The telephone company wants to add an area code composed of [#permalink]

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27 Oct 2013, 04:27
ronr34 wrote:
Bunuel wrote:

There are 2 left letters not 22.

So how do you get the answer?

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

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27 Oct 2013, 05:32
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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Re: The telephone company wants to add an area code composed of [#permalink]

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21 Feb 2015, 20:20
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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21 Feb 2015, 23:06
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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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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Current Student Joined: 21 Feb 2015 Posts: 10 Followers: 2 Kudos [?]: 3 [0], given: 11 Re: The telephone company wants to add an area code composed of [#permalink] ### Show Tags 22 Feb 2015, 08:44 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. GMAT assassins aren't born, they're made, Rich 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. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8344 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 382 Kudos [?]: 2474 [0], given: 164 Re: The telephone company wants to add an area code composed of [#permalink] ### Show Tags 22 Feb 2015, 13:03 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? GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: The telephone company wants to add an area code composed of   [#permalink] 02 Jul 2016, 18:57
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