Am I the odd man?

The sum of five consecutive odd numbers can be written as $(n - 4) + (n - 2) + n + (n + 2) + (n + 4) = 5n$ where $n$ is the middle number. $n = \frac{1185}{5} = 237$ And the greatest number of the five is equal to $n+4.$ $n + 4 = \boxed{241}$

The middle number or the third odd number of the 5 consecutive odd number equal to the average of the 5 consecutive odd number $\frac{1185}{5}$ =237.

Therefore, the greatest number or the 5th number is 4 more then the third number, which is equal to 237+4=241

Well, before attempting this question, we need to revise our elementary mathematics. The problem states the sum of five consecutive "ODD" numbers, right? So let's revise the general concept for odd numbers. Which is:

$EVEN+ODD=ODD.$

So the formula goes something like this:

$\Longrightarrow\quad 2n+(consecutive\quad odd\quad numbers)$

So now, let's add 5 consecutive odd numbers...

$\Longrightarrow\quad (2n+1)+(2n+3)+(2n+5)+(2n+7)+(2n+9)$ $\Longrightarrow\quad 10n+25=1185\quad (given\quad in\quad question)$

So, on further solving, we get $n=116$ .

Now, we're required to find the BIGGEST number out of the 5 consecutive odd numbers, so our BIGGEST odd number is $"2n+9"$ (obviously :P)

Hence, substituting the value of n back in our BIGGEST odd number.

$\Longrightarrow (2\times 116)+9=241.$

Hence the answer.