102002 is divisible by 4, 5 and 101001 but 2
isn't divisible by any of those, so  A, B and E are ruled out.

102002 + 2  is certainly divisible by 2, because 
both terms are even.

If you subtract 1 from any positive integer power of 10, 
you will always get a string of 9's.

Example:

100000000000000000
                -1
------------------
 99999999999999999


102002 + 2 = (102002 - 1) + 3 = [a string of 2002 9's] + 3.

That is divisible by 3 because any string of 9's is divisible by 3.

So 10^2002 + 2 is divisible by 6 since it's divisible by both 2 and 3.

So C is a correct answer.  But we should rule out D:

Any string of 9's is divisible by 9 but 3 isn't, so D is ruled out.

Answer: C 6

Edwin