The telephone company wants to add an area code composed of

Question

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

(A) 246 
(B) 248 
(C) 492 
(D) 15,128 
(E) 30,256

Bunuel · Accepted Answer

# 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.

jlgdr · Answer

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

icetray · Answer

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.

EMPOWERgmatRichC · Answer

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

icetray · Answer

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.

EMPOWERgmatRichC · Answer

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

ScottTargetTestPrep · Answer

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

poonam29 · Answer

rich , I used Permutation formula i.e. nPr = n!/(n-r)! for this question. Something like 124P2 - 122P2. But I got 490 as my answer. What am I missing here?

EMPOWERgmatRichC · Answer

Hi poonam29,

The prompt does NOT state that the 2 letters have to be 'different' - meaning that you could use the same letter for both "spots."

Thus, the number of different codes that could be created with 122 letters is (122)(122) and the number that could be created with 124 letters is (124)(124).

124^2 - 122^2 = 492

GMAT assassins aren't born, they're made,
Rich

Kinshook · Answer

Given:  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.

Asked:  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?

The number of additional area codes can be created if the company uses all 124 signs = 124*124 - 122*122 = 492

IMO C

Naif945 · Answer

Hello,

Can you explain why possible ways are 124*124 & 122*122 and not 124*123 & 122*121?

Thank You

Bunuel · Answer

Because each letter in the area code can independently be any of the signs, it is assumed that repeating signs is allowed. Thus, each position in the two-letter code can use the same set of signs fully. If repetition weren't allowed, the calculation would be different (e.g., 124*123). However, I agree that it should have been explicitly mentioned that repetition is allowed.

bumpbot · Answer

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The telephone company wants to add an area code composed of

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