The sum of two consecutive integers is 183. What is the smaller integer?

91

Explanation: Since the ones digit ends in a 3, that means the the ones digits of the two consecutive integers must be 1 and 2 or 6 and 7. However, you see 18 in the number 183. 9 + 9 = 18. When you add 6 and 7, you have to carry over one. However, when you add 1 and 2, you do not. Therefore, the two consecutive numbers are 91 and 92. 91 is the smaller integer, so that is the answer.