How many three-digit integers are exactly 17 more than a two-digit integer?
(A) 17
(B) 16
(C) 10
(D) 18
(E) 5
The smallest possible three-digit integer that is 17 more than a two-digit integer is 100 (100 is 17 more than 83 and 100 is in fact the smallest possible three-digit integer).

Notice that 101 is 17 more than 84,102 is 17 more than 85 , and so on. This continues until we reach 117 which is 17 more than 100, but 100 is not a two-digit integer. Thus, 116 is the largest possible three-digit integer that is 17 more than a two-digit integer (116 is 17 more than 99 ). Therefore, all of the integers from 100 to 116 inclusive, or 17 three-digit integers, are exactly 17 more than a two-digit integer.