+382 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?
+382 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.
+129852 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
+129852 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!!!
+382 I don't think you counted the 11 case. 2511 would also work because 2+5+1+1=9
