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A three-digit number N (in decimal) contains the digit 0. When the zero is removed, the resulting number is exactly N/9. What is the value of N?

Note: The number may contain more than one zero. The number may not begin with a zero. 

 Jul 6, 2020
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We have two options to consider: If the 0 that is removed is the middle digit or if 0 is the last digit.

Case 1: N=a0b

10a+b=(100a+b)/9

90a+9b=100a+b

8b=10a

4b=5a

b=5, a=4

Case 2: N=ab0

10a+b=(100a+10b)/9

90a+9b=100a+10b

10a=-b

The only answer for this is when a and b equal 0. But this number isn't a valid three digit number. 

So our answer is 405

 Jul 6, 2020

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