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

Answer: (A)

781

Answer 2

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.