This question requires us to use our knowledge of consecutive odd integers to generate an expression for their summed total. We will choose a variable to represent the initial odd integer and to this initial value we will add the first and second consecutive odd integers that follow. It is important to remember that after we have solved for x we must add 4 in order to arrive at the largest number in the set.
These integers can be represented as x, x + 2, and x + 4, from the smallest to the greatest, respectively. Their sum is 51, so mathematically speaking,
(x) + (x + 2) + (x + 4) = 51
We can combine like terms to find:
3x = 45.
We can divide both sides by 3, and get x = 15, which is the smallest number. The biggest number is x + 4 = 19.
The correct answer is (C).