+382 The four-digit numeral \(3AA1\) is divisible by 9. What digit does \(A\) represent?
+37146 Trial and error shows a = 0 1 2 3 4 5 6 do not work....but a =7 does work
+2863 The rule for divisibility for 9 is that all the digits add up to 9 or a multiply of 9, like 18.
So we can make an equation
3 + 2a + 1 = 9
4 + 2a = 9
Notice how a will NOT be an integer, so we try 18.
3 + 2a + 1 = 18
4 + 2a = 18
14 = 2a
a = 7
So A must be 7
+129852 If 3AA1 is divisible by 9, the sum of its digits must be divisible by 9
The means that
3 + 1 + 2A = 9M
4 + 2A = 9M
2A = 9M - 4
M must be an even number > 0
So
If
M = 2 A = 7
And 3771 / 9 = 419
+2863 Yes I learned something! I always thought of that the sum of the digits IS nine, now, from I learned from this problem.
