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 Quick divisibility (Posted on 2020-10-20)
Find all possible digits x, y, z such that the number 13xy45z is divisible by 792.

 No Solution Yet Submitted by Danish Ahmed Khan Rating: 5.0000 (1 votes)

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 Improved method? Comment 3 of 3 |
I agree with Math Man's answer, but slightly simpler (I think) is the following:

If 13xy456 is divisible by 99, then it is divisible by 9 and by 11.

In order to be divisible by 9, x + y = 8 or 17
In order to be divisible by 11, x - y = -3 or 8

By inspection,
If x + y = 17, then x - y cannot be -3 or 8
If x + y = 8, then x - y cannot be -8

So, x+y = 8 = x-y
The only solution is x = 8, y = 0

 Posted by Steve Herman on 2020-10-20 11:42:29
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