Question

What least number should be subtracted from 10003 to get a number exactly divisible by 11?
(a) 7
(b) 6
(c) 5
(d) 4

Answer 1

Hint: We will divide the number 10003 by 11 to find the remainder. The remainder is the number which when subtracted from the given number will give us a number which is exactly divisible by 11. Therefore, the remainder is the required number.

Complete step-by-step answer:
The number 10003 is not divisible by 11.
We have to find a number that we can subtract from 10003 so that the number is divisible by 11.
We will first divide the number 10003 by 11 and find its remainder.

Hence, we can say that the remainder is 4 and the quotient is 909.
If we will subtract the remainder from 10003, we will get a number that is exactly divisible by 11.
Therefore, $10003 - 4 = 9999$
Thus, the smallest number which is subtracted from 10003 so that it is exactly divisible by 11 is 4.
Hence, option (d) is correct.

Note: We can also check our final result by dividing the number that we get after subtracting the least number. That is $\dfrac{{9999}}{{11}} = 909$. Hence, 9999 is divisible by 11 and is 4 less than the given number. When the number is exactly divisible by any other number, then the remainder is 0.