Question

If the number 243x51 is divisible by 9, then the value of the digit marked as x would be
(A). 3
(B). 1
(C). 2
(D). 4

Answer 1

Hint: Here, we will be using the divisibility rule of 9 which states that “Sum of all the digits of the number, if divisible by 9 then that number will be divisible by 9.” So, we will here use this rule and will take the value of ‘x’ such that the number is in multiple of 9 from 0-9 digits.

Complete step-by-step solution -
In this question, we are asked to find what possible numbers are 0-9 which we put in 243x51 and that whole number will be divisible by 9.
Here, we will use the divisibility rule of 9. This rule states that “Sum of all the digits of the number, if divisible by 9 then that number will be divisible by 9.”
Now, we are given the number 243x51. Using this rule, we will add the digit present in number and see the total of the digit.
=x+15
Here, we know that 15 is multiple of 3 so, we have to select such values of x which when added to 15 gives the value in multiple of 9.
So, selecting the digit from 0-9 and checking the values.
Taking digit x=0 here, so, we get 0+15=15. So, 15 is not divisible by 9 therefore, x is not 0.
Similarly, here we can think logically that is adding 3 to 15 we get 18 which is multiple of 9. So, the value of x will be 3 as 15 + 3 will be 18. So, 3 is the one digit which is the answer.
Hence, the value of x is 3 which when kept in 243x51 will be divisible by 9.
Option (a) is correct.

Note: Students should be sure with the divisibility rule of 9 as, there are many such rules to be remembered. So, it might get confused and there are chances of mistakes. Another way of doing this is by taking the value of ‘x’ from 0-9 and checking the result by putting x=0,1,2,3,…9. This will become very tedious and time consuming. So, it's better to go with divisibility rules as it becomes easier to solve.