Find the smallest number to be added to 999 so that 99 divides the sum exactly.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 90.
Let the smallest number added in 999 be x
So,
⇒ 999 + x = 0
Let's divide 999 by 99 to find the remainder
⇒ 999/99 = 10, 9(remainder)
This means 999 leaves a remainder of 9 when divided by 99
To make 999 + x divisible by 99, we need to "cancel out" the remainder of 9
This means we need to add x = 99 − 9 to reach the next multiple of 99.
⇒ x = 99 - 9
⇒ x = 90
Now, we add 90 to 999
⇒ 999 + 90 = 1089
Then, we check if 1089 is divisible by 99
⇒ 1089/99 = 11
Thus,
The smallest number to be added to 999 so that the sum is divisible by 99 is 90.