The median of a set of consecutive odd integers is 138. If the greatest integer in the set is 145, what is the smallest integer in the set?
To find the median of a set of consecutive odd integers, I need to know how many integers there are in the set and where the middle one is. Since the greatest integer is 145, I can work backwards and subtract 2 from each term until I reach the middle one. If I do that, I get 145, 143, 141, 139, 137, 135, 133, and 131. That's eight integers in total, so the middle one is the average of the fourth and fifth ones, which is 138 as given. Therefore, the smallest integer in the set is 131. 