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telephone extensions

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by uptowngirl92 » Mon Jun 08, 2009 5:23 am
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have?

(A) 4 (B) 6 (C) 12

(D) 16 (E) 24

[spoiler]OA:(c)[/spoiler]

The wording of the problem itself is not clear.I could'nt figure out what we are supposed to find in the first place?Nevertheless I answered 4!=24 which is wrong.Can someone please shed some light?
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by tohellandback » Mon Jun 08, 2009 5:44 am
answer:12
explanation:
since the extension has to be an even number and all the 4 digits have to be used. The number has to end with 2 or 6. (if you think of ending it with 0,4, or 8, you will not be able to use all the 4 given digits coz we are left with only 3 places)
numbers are of the form
XYZ2
or XYZ6
total 12 options we have.

Thanks
The powers of two are bloody impolite!!
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