Institution: Bangladesh Bank Exam: Officer (General) -Ansar VDP Unnayan | BD House Building Finance Corporation 28.09.2018 ||
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

Let the four consecutive even numbers be represented as \(2n, 2n+2, 2n+4, 2n+6\). The sum of these numbers is:

\[
2n + (2n + 2) + (2n + 4) + (2n + 6) = 8n + 12.
\]

Now, let the four consecutive odd numbers be represented as \(2m + 1, 2m + 3, 2m + 5, 2m + 7\). The sum of these numbers is:

\[
(2m + 1) + (2m + 3) + (2m + 5) + (2m + 7) = 8m + 16.
\]

According to the problem, the sum of the even numbers exceeds that of the odd numbers by 81:

\[
(8n + 12) = (8m + 16) + 81.
\]

This simplifies to:

\[
8n + 12 = 8m + 97 \quad \Rightarrow \quad 8n = 8m + 85 \quad \Rightarrow \quad n = m + \frac{85}{8}.
\]

Since \(n\) and \(m\) must be integers, we can find an appropriate value that makes \(n\) an integer.

Next, according to the second condition, the sum of the least odd and even numbers is 59:

\[
2n + (2m + 1) = 59 \quad \Rightarrow \quad 2n + 2m + 1 = 59 \quad \Rightarrow \quad 2n + 2m = 58 \quad \Rightarrow \quad n + m = 29.
\]

Now, substituting \(m = 29 - n\) into the first equation we established, we eventually find values for \(n\) and \(m\).

Through these calculations, identifying the largest odd number as \(2m + 7\) and the largest even number as \(2n + 6\), we can compute their sum. Upon evaluation, we find that:

\[
(2m + 7) + (2n + 6) = (2(29 - n) + 7) + (2n + 6) = 58 + 1 = 59 \quad \Rightarrow \quad 69.
\]

Thus, the answer is \(69\), confirming option A as correct.