Beat The GMAT

vineetbatra · Wed Oct 28, 2009 2:32 pm

32. 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

Will post OA later

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NikolayZ · Wed Oct 28, 2009 3:48 pm

hey Vineet!

I assume that the code can consist of 2 similar sings (AA, BB)

We know that 2 signs are unused.

1) 2 signs can be themselves 2!=2 codes, plus 2 (AA and BB), 4 overall.
2)
(a)With 2 unused signs we have 2 different first signs and 2 latter ones ( 2*2=4).
(b)We have another 122 signs to be the first or the second sign of the code. Combined with (a) we have 4*122 possibilities.
So, 122*4+4=492.

I think the answer is C.