Question

Replace the star (*) in $394*7$ so that it may be divisible by 9.

Answer 1

Hint: For a number to be divisible by 9, the number of the digits in the number must also be divisible by 9. Here, in the question, the number is not complete, and we need to determine the missing digit in the number so that the resultant number is divisible by 9.

Complete step-by-step solution
The given number is 394*7. For the number to be divisible by 9, the sum of the digits must also be divisible by 9.
The sum of the digits of the number is $3 + 9 + 4 + * + 7 = 23 + *$
So, $23 + *$ to be divisible by 9, the sum should be $27$ as 27 is nearest to 23 which is divisible by 9.
Hence,
$
  23 + * = 27 \\
  * = 27 - 23 \\
  * = 4 \\
$
So, the value of the star (*) in the number 394*7 so that the number is divisible by 9 is 4.

Note: Students must be aware of the different divisibility rules for the numbers to be divisible by any integer. In general, there are defined divisibility rules for the single as well as double-digit numbers. Here, in the question, we have taken the nearest number 27 which is divisible by 9 because if we have taken higher multiples of 9 then the value of the star (*) will result in a two-digit number which should not be and if we have taken lower multiples of 9 then, the value of star (*) is negative.