Ram wrote first 50 natural numbers on a blackboard. Then he erased two numbers say p and q, and replaced them by a single number N. He performed this operation repeatedly until a single number was left. For all odd values of n, in the n th operati…

Ram wrote first 50 natural numbers on a blackboard. Then he erased two numbers say p and q, and replaced them by a single number N. He performed this operation repeatedly until a single number was left. For all odd values of n, in the n th operation, he chose N to be p+q+1 and for all even values of n, he chose N to be p+q-1. Find the final number which remained.

- 1225
- 1276
- 1275
- 1274

0 voters

I think the answer is 1275 not sure.

i give my explanation. take for example upto 5 natural numbers 1,2,3,4,5.

Take p=1, q=2

when u remove 1&2, u have to replace it with 3(n=p+q) which is an odd number. so u have to replace it with 4(if n is odd then n=p+q+1) by **adding 1** with 3. now 1&2 is replaced with 4. now the series become 4,3,4,5

when u remove 4&3, u have to replace 7 which is an odd number. so u have to replace it with 8 by

**adding 1 **with 7. now 4&3 is replaced with 8. now the series become 8,4,5

when u remove 8&4, u have to replace 12 which is an even number. so u have to replace it with 11 by **subtracting 1** from 12. now 8&4 is replaced with 11. now the series become 11,5

when u remove 11&5, u have to replace 16 which is an even number. so u have to replace it with 15 by** subtracting 1 **from 16. now 11&5 is replaced with 15. now the series become 15

Hence for this 5 natural numbers, there is addition of 1 for two times and subtraction of 1 for two times consecutively. by adding these 5 natural numbers the total value is 15 and what we get after the procedure is also 15.

Therefore when we proceed the above procedure for 50 natural numbers, all the 1's that are added will be deleted. hence we may get the result as of by adding the 50 numbers. i.e. 1275.

Ram wrote first 50 natural numbers on a blackboard. Then he erased two numbers say p and q, and replaced them by a single number N. He performed this operation repeatedly until a single number was left. For all odd values of n, in the n th operation, he chose N to be p+q+1 and for all even values of n, he chose N to be p+q-1. Find the final number which remained.

1) 1275

2) 1276

3) 1274

4) 1225 Skip

×

Oops, choose atleast 1 option here

I think the answer is 1275 not sure.

i give my explanation. take for example upto 5 natural numbers 1,2,3,4,5.

Take p=1, q=2

when u remove 1&2, u have to replace it with 3(n=p+q) which is an odd number. so u have to replace it with 4(if n is odd then n=p+q+1) by **adding 1** with 3. now 1&2 is replaced with 4. now the series become 4,3,4,5

when u remove 4&3, u have to replace 7 which is an odd number. so u have to replace it with 8 by

**adding 1 **with 7. now 4&3 is replaced with 8. now the series become 8,4,5

when u remove 8&4, u have to replace 12 which is an even number. so u have to replace it with 11 by **subtracting 1** from 12. now 8&4 is replaced with 11. now the series become 11,5

when u remove 11&5, u have to replace 16 which is an even number. so u have to replace it with 15 by** subtracting 1 **from 16. now 11&5 is replaced with 15. now the series become 15

Hence for this 5 natural numbers, there is addition of 1 for two times and subtraction of 1 for two times consecutively. by adding these 5 natural numbers the total value is 15 and what we get after the procedure is also 15.

Therefore when we proceed the above procedure for 50 natural numbers, all the 1's that are added will be deleted. hence we may get the result as of by adding the 50 numbers. i.e. 1275.