The integers 1,2,...... 40 are written on a 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 is the number left on the board at the end? (CAT 2007)

820

No worries! We‘ve got your back. Try BYJU‘S free classes today!

821

No worries! We‘ve got your back. Try BYJU‘S free classes today!

781

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

819

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 781
Here, in each step we are adding two numbers and reducing the sum by 1. So after 39 operations, we will have the sum of all the numbers from 1 to 40 reduced by 39. Hence the final number will be $S_{40} - 39 = 781.$

Suggest Corrections

Similar questions

The integers 1,2,….. 40 are written on a 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 is the number left on the board at the end?

Q. The integers 1, 2, . . ., 40 are written on a black board. 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 ends?

Q. The integers 1-40 are written on a blackboard. The following operation is then repeated 39 times. In each repetition, any pair of numbers (say a and b) are erased and a new number (a + b – 1) is written in its place. What will be the number left on the board at the end?

Q. The integers 1,2,3,4,......n are written on a blackboard. The following operation is then repeated until we will get only one number: In each repetition, any two numbers say a and b, currently on the blackboard are erased and a new number a + b is written. But one number was missed by mistake. The sum obtained was 1525. Which number was missed?

Q. The integers 1,2,.........64 are written on a blackboard. The following operation is repeated 63 times: Any 2 numbers are chosen out of these 64 numbers and replaced with a number equal to 1 minus the sum of 2 numbers. What will be the number left over on the board after 63 operations?

Join BYJU'S Learning Program

The integers 1,2,...... 40 are written on a 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 is the number left on the board at the end? (CAT 2007)

The correct option is C 781Here, in each step we are adding two numbers and reducing the sum by 1. So after 39 operations, we will have the sum of all the numbers from 1 to 40 reduced by 39. Hence the final number will be S40−39=781.

The correct option is C 781
Here, in each step we are adding two numbers and reducing the sum by 1. So after 39 operations, we will have the sum of all the numbers from 1 to 40 reduced by 39. Hence the final number will be $S_{40} - 39 = 781.$