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A number when divided by 100 leaves a quotient (Q) and a
remainder (R). How many three-digit natural numbers are
there such that Q + R is divisible by 11?
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Answer Posted / arthi
Some people say its 90 numbers, and some say that its 81.
The correct answer depends on the real definition of natural numbers.
Wikipedia says:
It is either the set of positive integers {1, 2, 3, ...} according to the traditional definition or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the nineteenth century.
Assuming the former is correct, {1, 2, 3, ...} the answer is 81. (Checking between 100 and 999)
Whereas assuming the latter is correct {0, 1, 2, ...}, the answer is 90. (Checking between 1 and 999)
Now, for finding the answer, just know if Q+R is div by 11, and Q is the digit in the hundred's place, then the three digit number itself is div by 11. (The explanation is lengthy, so Im not including it now. I might post it later.)
so only find the number of numbers divisible by 11, between 1 and 999 or 100 and 999 as the case may be.
The answer 90 in the first case, and 81 in the second case.
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