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Integers

by shashank.ism » Mon Feb 08, 2010 7:21 am
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 will be the number left on the board at the end?

a) 820
b) 821
c) 781
d) 819
e) 780
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by harsh.champ » Mon Feb 08, 2010 7:28 am
shashank.ism wrote: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 will be the number left on the board at the end?

a) 820
b) 821
c) 781
d) 819
e) 780
Suppose a=2,b=3 the new no. will be 2+3 -1 =4 So for each operation ,we are losing 1.
For 39 operations we will lose 39.
Sum of 1st 40 no.s are 40(40+1)/2 = 820
[spoiler]820-39 = 781. C[/spoiler]
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by ajith » Mon Feb 08, 2010 11:02 am
shashank.ism wrote: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 will be the number left on the board at the end?

a) 820
b) 821
c) 781
d) 819
e) 780
The number written in the end will be = 1+2+3+4+...40 -39

40*41/2-39 = 781
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