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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] New post 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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 [#permalink] New post 20 Sep 2005, 09:58
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] New post 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!
J :)
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Re: The telephone company wants to add an area code composed of [#permalink] New post 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.

Answer: C.

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

Answer: C.

Similar questions to practice:
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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] New post 26 Oct 2013, 02:36
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.

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
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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?


There are 2 left letters not 22.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The telephone company wants to add an area code composed of [#permalink] New post 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] New post 27 Oct 2013, 04:27
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Re: The telephone company wants to add an area code composed of [#permalink] New post 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.
Re: The telephone company wants to add an area code composed of   [#permalink] 27 Oct 2013, 05:32
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