Rocky thinks of an odd integer adds the next two consecutive integers which of these could be the sum a) 44560
b)44561
c)44562
d)44563

Step-by-step explanation:

First, we have to prove that the sum of 3 consecutive integers is a multiple of 3.

Let x be the smallest of the 3 consecutive integers. We have (x + 1) and (x + 2) as our other consecutive integers.

Notice that x + (x + 1) + (x + 2) = 3x + 3 = 3(x + 1), which is a multiple of 3.

Hence we have proven our point. Back to the question:

The possible sum has to be a multiple of 3. Searching the options, only 44562 is a multiple of 3. (44562 / 3 = 14854) Hence 44562 is the answer. (C)