What is the smallest of five consecutive odd integers whose sum is S?
A. (S - 20)/5
B. 5S + 20
C. (S + 20)/5
D. (S + 12)/5
E. 5S - 20
Let the smallest of the five consecutive odd integers be m. Then, m + (m + 2) + (m + 4) + (m + 6) + (m + 8) = S or 5m + 20 = S.
Thus, m = (S - 20)/5.
If you are not at ease with the algebra, another strategy may be adopted.
Choose an easy set of five consecutive odd integers, e.g., 1, 3, 5, 7, 9.
Their sum S = 25. Next, substituting S = 25, evaluate the given choices.
Only (S - 20)/5 = (25 - 20)/5 = 1 (the smallest integer chosen).