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avatar+196 

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

 Oct 4, 2019
 #1
avatar+19832 
+4

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

 Oct 4, 2019
 #2
avatar+2417 
+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
avatar+196 
+2

Thank you for your answers.

hellospeedmind  Oct 4, 2019
 #4
avatar+104962 
+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

 

cool cool cool 

 Oct 4, 2019
 #5
avatar+2417 
+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

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