Given a three digit number $x , 5 , y$ where $x$ is the digit at the hundred place and $y$ is the digit ones. If the number $x + 5 + y$ is divisible by 9, find the least possible value $x + y$?
Hint: Divisibility rule is a kind of shortcut to figure out if a given integer is divisible by a divisor, without performing the whole division process but by examining its digits. Multiple divisibility rules can be applied to the same number which can quickly determine its prime factorization.
Complete step by step solution: Given, $x + 5 + y$ Divisibility Rule of 9: The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number are divisible by 9, then the number itself is divisible by 9. By definition of divisibility rule of 9 the sum of the integer must be equal to 9 then $ \Rightarrow x + 5 + y = 9$ Now simplify the equation, $ \Rightarrow x + y = 9 - 5$ $ \Rightarrow x + y = 4$ Hence the least possible value for $x + y$ is 4.
Note: Divisibility rules are of great importance while checking the prime numbers. These are handy to solve word problems. They are useful to do quick calculations. Divisibility means that you are able to divide a number evenly. There are other rules to check the number divisibility from 2 to 13.