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The sum of all natural numbers 'n' such ...

The sum of all natural numbers 'n' such that `100 lt n lt 200 and HCF (91, n) gt 1` is

A

3203

B

3303

C

3221

D

3121

Text Solution

Verified by Experts

The correct Answer is:
D
The natural numbers between 100 and 200 are 101, 102, 103, …, 199.
Since, `91=13 xx 7`, so the natural numbers between 100 and 200 whose HCF with 91 is more than 1 are the numbers which are either divisible by 7 or 13.
So, the required sum of numbers between 100 and 200 = (sum of numbers divisible by 7) + (sum of numbers divisible by 13) - (sum of numbers divisible by 91)
`=sum_(r=1)^(14)(98+7r)+sum_(r=1)^(8)(91+13r)-(182)`
`=(98xx14)+7((14xx15)/(2))+(91xx8)+13((8xx9)/(2))-(182)`
`=1372+735+728+468-182`
`=3303-182=3121`
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