Posted by Eleana M on Tuesday, February 1, 2011 at 6:20pm.
You are looking for the smallest number N that satisfies
N mod 4 = 2, ....(1)
N mod 5 = 1 .....(2)
Since N mod 4 = 2 can only be satisfied by an even number, N can only be a number that ends in the digit 6 if (2) is to be satisfied.
Since it is over 10, and 16 does not satisfy (1), we choose 26 as the smallest number over 10 that satisfies the two given conditions.
For a formal treatment of this class of problems, look up the "Chinese remainder theorem".
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