Question

if the number 41536* is completely divisible by 72 then what will be the digit numbers in the place of *

Answer 1

72 = 8 × 9

  ⇒ A number is divisible by 8 if the no. formed by last three digits is divisible by 8.

  ⇒ If the sum of digits of a number is divisible by 9, then so will be the number.

So what about 72?!

If the number formed by the last three digits of a number is divisible by 8 and the sum of the digits of the number is divisible by 9, then the number is divisible by 72.

Consider the number 41536x.   (Taking * as x)

  → 41536x will be divisible by 8 if 36x is divisible by 8.

  → 41536x will be divisible by 9 if  4 + 1 + 5 + 3 + 6 + x  =  x + 19  is divisible by 9.

According to the second condition, there is only 1 possible value for x. So there's no need to consider the first condition.

x + 19 could be divisible by 9, and it is true that 27, a multiple of 9, is the lowest possible multiple of 9 which is greater than 19.

Thus we can state that x + 19 = 27, therefore x = 8.

If we consider x + 19 = 36, x becomes 17, and x can't be a two digit number as x is a digit of the number 41536x. That is wy there's only 1 possible number for x.

Thus, the value of x is 8.