Question

The integers \(1, 2 ... 40\) are written on the blackboard. The following operation is then repeated 39 times. In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number \(a+b-1\) is written. What will be the number left on the board at the end?

• A. 781
• B. 780
• C. 819
• D. 820
• E. 821

Answer 1

The Correct Option is A

Given that the integers \(1, 2, 3 … 40\) are written on the blackboard. Any two numbers, say a and b, are erased and a new number \(a + b – 1\) is written. This operation is repeated 39 times. 
In this manner, the numbers \(1, 2, 3 … 40\) are added and 1 is subtracted 39 times. 
So, number left on the blackboard
=\(1, 2, 3 … 40-(39\times1)\)
\(=\frac{40\times41}{2}-39\)
\(=20\times41-39\)
\(=820-39=781\)
So,The correct answer is A.