The four-digit numeral \(3AA1\) is divisible by 9. What digit does \(A\) represent?

hellospeedmind Oct 4, 2019

#1**0 **

Trial and error shows a = 0 1 2 3 4 5 6 do not work....but a =7 does work

ElectricPavlov Oct 4, 2019

#2**+3 **

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

CalculatorUser
Oct 4, 2019

#4**+3 **

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

CPhill Oct 4, 2019

#5**+2 **

Yes I learned something! I always thought of that the sum of the digits IS nine, now, from I learned from this problem.

CalculatorUser
Oct 4, 2019