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Two Digit Integers (Posted on 2006-07-14) Difficulty: 4 of 5
Find all possible two digit positive integers N for which the sum of digits of 10N - N is divisible by 170.

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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re: Solution | Comment 5 of 11 |
(In reply to Solution by Dej Mar)

Hi,

I am unsure about the solutions here...20,39,58,77,96.  Not have a calculator so I can't give the full numbers but my thinking goes like this:

1) To be divisible by 170, the last digit of this number has to be zero.  It needs to be a multiple of ten.

2) 10 to any power (X) will be a multiple of ten. If you then subtract that number,  you will then only have a result multiple of ten if X is a multiple of ten.

Therefor: 20 could be a posible solution, but 39,58,77,96.

This disagrees with multiple comments.  What am I missing?

Patrick


  Posted by Patrick on 2006-07-18 13:39:29
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