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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 / nij
rule1: Number is divisible by 11 only when difference of
sumation of numbers at odd and even place is either 11 or 0.
e.g. 352 is divisible by 11 as (3+2) - 5 = 0
so Q+R would be divisible by 11 only when it satisfies rule1
upto 100 there are 9 numbers 11,22,33,44,55,66,77,88,99.
don't consider this...since 3 digit natural numbers are asked
From 100 to 200. Q would be 1 and reminder(R)need to be 10,
21,32,43,54,65,76,87,98 again 9 numbers.
From 200 to 100. Q would be 2 and R need to be
9,20,31,42,53,64,75,86,97 again 9 numbers.....
LIKEWISE
100 to 200----9 numbers
200 to 300----9 numbers
300 to 400----9
400 to 500----9
500 to 600----9
600 to 700----9
700 to 800-----9
800 to 900-----9
900 to 1000 ---9
so total 9x9=81 numbers
| Is This Answer Correct ? | 41 Yes | 2 No |
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