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avatar+355 

The four-digit number \(25AB\) is divisible by nine, with \(A\) the tens digit and \(B\) the units digit. How many such four-digit numbers could \(25AB\) represent?

 Oct 4, 2019
 #1
avatar+355 
+1

For AB I got 11, 02, 20, 29, 38, 47, 56, 65, 74, 83, and 92. I'm not sure if that's all of them.

 Oct 4, 2019
 #2
avatar+109563 
+2

25AB

 

The sum of the digits must be a multiple of 9......so.....

 

2 + 5  +  A  + B  =   9M

 

A + B   =  9M - 7

 

If  M =  1                    M  =  2                M  = 3

A + B  =  2                A + B  =  11         A + B  = 20 

A , B  =                     A , B =                 No possibilities  for A, B when  M > 2

0, 2                           2, 9

and the reverse        3, 8

                                 4, 7

                                 5, 6

                                 and the reverses

 

So....by my count.....we have 5(2) =  10 such numbers

 

 

cool cool cool

 Oct 4, 2019
 #3
avatar+109563 
+2

If A,B  can be the same integers....you are correct, HSM  !!!

 

[ I assumed that they must be unique ]

 

Whatever.....our answers only differ by 1, so  it probably depends upon our assumptions  ....LOL!!!

 

 

 

 

cool cool cool

CPhill  Oct 4, 2019
 #4
avatar+355 
+2

I don't think you counted the 11 case. 2511 would also work because 2+5+1+1=9

hellospeedmind  Oct 4, 2019
 #5
avatar+355 
+2

Ok. Thank you for your answer

hellospeedmind  Oct 4, 2019
 #6
avatar+109563 
0

Yep...if A,B  can be the same integers, you are correct

 

[ I assumed that they had to be different ]

 

 

cool cool cool

CPhill  Oct 4, 2019

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