Beat The GMAT

sreak1089 · Wed Jan 20, 2010 1:18 am

A telephone company wanted 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) 15128
E) 30256

Recommend this topic

Back to top

fibbonnaci · Wed Jan 20, 2010 1:53 am

each letter can take 122 different signs.
total ways of forming 2 letters is 122*122

Now if the company wants to use 124 signs, then for 2 letters ,
total number of ways = 124*124.

Difference= (124)^2 - (122)^2
= (124+ 122) (124-122)
= 246*2 => 492 additional area codes can be created.

Answer = C

Back to top

sreak1089 · Wed Jan 20, 2010 8:55 am

I am not able to figure out, how you got 122*122? can you please elaborate?

Is it because, you have 122 signs for the first letter and for each of the 122 letters you can have further 122 signs right?

To make it simple, let's say you have only 3 symbols (assume a, b, c) if you have two letter code then you have:

aa ba ca
ab bb cb
ac bc cc

Thus, 3 * 3 = 9 ways.

I thinking I am getting it, Am I correct?[/img]