+0

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

+4
215
5
+333

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

Oct 4, 2019

#1
+19879
0

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

Oct 4, 2019
#2
+2547
+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
#3
+333
+2

hellospeedmind  Oct 4, 2019
#4
+106539
+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

Oct 4, 2019
#5
+2547
+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