# SOLUTION: The number 10^2002 + 2 is divisible by A 4 B 5 C 6 D 9 E 10^1001

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 Click here to see ALL problems on Divisibility and Prime Numbers Question 477530: The number 10^2002 + 2 is divisible by A 4 B 5 C 6 D 9 E 10^1001 Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!```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```