Question

1st 126 natural numbers are put side by side in the ascending order to form a large number What will be the remainder when this number is divided by 5625?​

Answer 1

Answer: (c) 126

Explanation:

5625 = (75)^2 = (25)*(25)* (3) *(3)

So, let us find out divisibility by 125 and 9.

For 9, sum of digits should be 9.

1234..9 => Sum of 1 to 9 = 45 => Divisible by 9

10111213..99 => Sum id divisible by 9

Going in similar manner, we get that sum till ....125126 is divisible by 9. So, number is divisible by 9.

Now, by observation, if we remove last 3 digits i.e. 126 and replace them with zeros (i.e. subtract 126), number will end in 125000 which is divisible by 125 as well as 9. Note that, we can subtract 126 as 1+2+6=9.

So, if we subtract 126 number is divisible by 125 and 9. 125 and 9 are co-primes. So, number will be divisble by 125*9 i.e 5625.

So, remainder = 126