N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 26th digit?  Pick one
A) 5 B) 6 C) 1 D) 2 E) 3
DETAILED SOLUTION   To begin with, the question should read "find the 44th digit".   Any number of the form abcabc is a multiple of 1001. 1001 is 7 * 11 * 13. So, any number of the form abcabc is a multiple of 13.   So, a number comprising 42 2's would be a multiple of 13, so would a number comprising 36 2's. So, in effect, we are left with a two digit number 2a, where a is the 44th digit. 26 is a multiple of 13, so the 44th digit should be 6.   CORRECT ANSWER 6
<result>B</result>
N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 26th digit?