Question

If 9A987B6 is divisible by 18, then the smallest value for A+B is___.

Answer 1

Answer:

To solve such questions, you must have the knowledge of divisibility rules for some common numbers.

Here, you want to make the number divisible by 18.

take prime factors of 18 first.

18 = 2 * 3*3

or, 18 = 2 * 9

Now, the given number must be divisible by 2 and 9 completely.

The divisibility rule for 2  is that the number should be even.

The divisible rule for 9 is that the number must be completely divisible by 9.

Take the number now.

9A987B6

The sum of the number is 39 + A + B

Now you know  that multiples of 9 are 36, 45, 54.

However, the number is greater than 36.

So, we will add something in 39 to make it 45. But , then if the number becomes 45, it will not be divisible by 2. So, we cannot make the number 45 or add 6 to the the number or take the value of A + B as 6.

Now,  the next multiple of 9 is 54.

So, you know that 54 is completely divisible by 2 and also by 9.

Therefore, you must take the value of A + B as 15. So, 39+ 15 = 54

So, the smallest value of A+B  = 15, which makes the number completely divisible by 18.

Answer - 15