Question

If a three-digit number 89y is divisible by 9 what might be the values of y?

Answer 1

Hint: We know that in the divisibility test of 9, the sum of all the digits of a number on which the divisibility test has been applied should be divisible by 9 so it is given that 89y is divisible by 9 so the sum of 8, 9 and y are divisible by 9. On adding the numbers 8, 9 and y will give you a number which has y in it so by hit and trial method see substituting which value of y will give the number which is divisible by 9.

Complete step-by-step solution:
We have given a three-digit number 89y which is divisible by 9.
We know that a number is divisible by 9 when the sum of all the digits of the number is divisible by 9.
The three-digit number given in the above problem is 89y which has 3 digits 8, 9, and y so adding these three digits we get,
$\begin{align}
  & 8+9+y \\
 & =17+y \\
\end{align}$
The addition of the digits is giving us a number like $17 + y$. Now, this number is divisible by 9 if we put y as 1 here then the number $17 + y$ becomes:
18
We know that 18 is divisible by 9 by 2 times.
Hence, the possible value of y in $89y$ is 1.

Note: You might think that the value of y can be 10 also because when we substitute the value of y as 10 in $17 + y$ then the number is 27 and which is divisible by 9 but the catch here is that y is a single-digit number and the value of y that we have got here is 10 which is a two-digit number so y cannot be 10.