Question

If $ 2791A $ is divisible by $ 9 $ , supply the missing digit in place of ---?

Answer 1

Hint: First, we will need to know about the divisibility rule of the number nine.
The number nine will only divide three digits or more than the three digits number when the sum of the numbers should need to be divisible by the number nine.
Suppose if the number is given as $ 333 $ then the sum of the number is $ 3 + 3 + 3 = 9 $ hence this number will be divisible by the nine. To check this, we apply the divisibility that $ \dfrac{{333}}{9} = 37 $ .
Hence the rule for divisibility of the number nine.

Complete step by step answer:
   Given that, $ 2791A $ is the number which is a five-digit number, so we are able to apply the divisibility rule.
But in this given number there is an unknown value A, without that we cannot apply the rule.
So first find the value A, by taking the sum of the digits we get $ 2791A \Rightarrow 2 + 7 + 9 + 1 + A $ and this value will need to be divisible by the number nine is the required answer.
From adding the terms we get $ 2 + 7 + 9 + 1 + A = 19 + A $ which is the generalized form.
Since there is $ 19 $ and in what number if we add the nineteen, we get the divisibility of the nine, if we substitute the $ A = 2 $ , then we get $ 21 $ which is not divisible by nine.
Hence the least possibility of getting the number is $ A = 8 $ to apply this in the above value we get, $ 19 + A = 19 + 8 \Rightarrow 27 $ which will divide the number nine as three.
Hence the $ A = 8 $ is the missing digit.
Or we can simply find this using the division property that $ 19 + A = 27 $ (after nineteen the possibility that number nine division is twenty-seven)
Hence, we get, $ 19 + A = 27 \Rightarrow A = 8 $

Note: We must know about the divisibility rule of the number nine, so we are simply able to solve this.
We may be confused when two digits this rule is applied or not, but the digits need to be three or more than three for sure to apply the given rule for number nine.
We don’t need to get exactly the number nine as the sum of the numbers, the sum of the numbers will need to be divided by the number.
Hence $ \dfrac{{666}}{9} = 74 $ and $ 6 + 6 + 6 = 18 $ which is also divisible by nine.