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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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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, 07:37, edited 1 time in total.
Edited the question and added the OA.

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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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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!
J :)

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

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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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Hope this 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.

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
baker-s-dozen-128782-20.html#p1057502
in-a-certain-appliance-store-each-model-of-television-is-136646.html
m04q29-color-coding-70074.html
john-has-12-clients-and-he-wants-to-use-color-coding-to-iden-107307.html
how-many-4-digit-even-numbers-do-not-use-any-digit-more-than-101874.html
a-certain-stock-exchange-designates-each-stock-with-a-85831.html
the-simplastic-language-has-only-2-unique-values-and-105845.html
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?

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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:
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
baker-s-dozen-128782-20.html#p1057502
in-a-certain-appliance-store-each-model-of-television-is-136646.html
m04q29-color-coding-70074.html
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how-many-4-digit-even-numbers-do-not-use-any-digit-more-than-101874.html
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the-simplastic-language-has-only-2-unique-values-and-105845.html
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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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, 09:01
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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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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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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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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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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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)?
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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] 21 Sep 2017, 14:55
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