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

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20 Sep 2005, 10:20

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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?

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

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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

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

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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.

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

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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.

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

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26 Oct 2013, 03:36

Expert's post

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.

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

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23 Nov 2014, 11:20

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

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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.

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

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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.

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.

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

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22 Feb 2015, 14:03

Expert's post

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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