The sum of three consecutive odd numbers is 1383 . What is the largest number? (a) 463 (b) 49 (c) 457 (d) 461 (e) None of these

To find the three consecutive odd numbers whose sum is 1383, let’s denote the smallest of these numbers as \(n\), the next one as \(n + 2\), and the largest as \(n + 4\) (since odd numbers differ by 2).

The sum of these numbers is given as:
\[n + (n + 2) + (n + 4) = 1383\]

Simplifying, we get:
\[3n + 6 = 1383\]

Subtracting 6 from both sides:
\[3n = 1377\]

Dividing by 3:
\[n = 459\]

So, the three consecutive odd numbers are 459, 461, and 463. The largest number among them is \(463\).

Therefore, the correct answer is (a) 463.