GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Aug 2019, 20:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 18 Aug 2005
Posts: 80
Location: Italy, Rome caput mundi
The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

Updated on: 25 Oct 2013, 07:37
4
35
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:10) correct 38% (02:20) wrong based on 409 sessions

### HideShow timer Statistics

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

_________________
"To win the battle you need to last 15 minutes longer than your enemies"

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.
Math Expert
Joined: 02 Sep 2009
Posts: 57279
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

25 Oct 2013, 07:41
8
8
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
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.
_________________
##### General Discussion
Manager
Joined: 15 Jul 2005
Posts: 97

### Show Tags

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

124^2-122^2

http://www.gmatclub.com/phpbb/viewtopic.php?t=20091
SVP
Joined: 06 Sep 2013
Posts: 1626
Concentration: Finance
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

25 Oct 2013, 05:22
1
1
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
Senior Manager
Joined: 08 Apr 2012
Posts: 333
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 57279
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

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.

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?

There are 2 left letters not 22.
_________________
Manager
Status: Joining Cranfield Sep 2014
Joined: 01 Sep 2012
Posts: 50
Concentration: Technology, General Management
GMAT 1: 530 Q50 V14
GMAT 2: 630 Q48 V29
WE: Engineering (Energy and Utilities)
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

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.
Intern
Joined: 21 Feb 2015
Posts: 10
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

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.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14867
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

22 Feb 2015, 00:06
1
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Intern Joined: 21 Feb 2015 Posts: 10 Re: The telephone company wants to add an area code composed of [#permalink] ### Show Tags 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. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14867 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The telephone company wants to add an area code composed of [#permalink] ### Show Tags 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? GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7467
Location: United States (CA)
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 14 Feb 2015
Posts: 23
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

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.
_________________
Intern
Joined: 31 Jan 2018
Posts: 16
Re: The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

17 Feb 2018, 03:44
Total Number of 2 letter codes possible=124^2
Number of codes formed using 122 letters=122^2
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2967
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
The telephone company wants to add an area code composed of  [#permalink]

### Show Tags

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 $$= 124^2 - 122^2 = (124+122)*(124-122) = 246*2 = 492$$

To attend the !!!FREE!!! Live class on Permutation and combination on 24th July 2019 @9 PM IST by clicking and registering on the LINK

.

.
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
The telephone company wants to add an area code composed of   [#permalink] 23 Jul 2019, 08:21
Display posts from previous: Sort by