Question

find the sum of integers between 100 and 200 that are divisible by 100

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Answer 1

Interpretation 1: Let a and b be integers divisible by 100 between 100 and 200.

Multiples of 100 are 100, 200, 300 ....

There is no multiple of 100 between 100 and 200.

So, no such integer or sum exists.

Interpretation 2: Let a and b be integers between 100 and 200. (a+b) should be divisible by 100.

Since (100+200)=300 is divisible by 100

All integers a and b of the form (100+x) and (200-x) where x is a natural number ≤ 99

(a+b) = 100+x+200-x = 300

300 is divisible by 100. So is (a+b)

For eg 101+199

102+198

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149+151

150+150