what is the smallest possible integer d for which 2009 + d ​ is a multiple of 11?

 

Does d have to be positive?  

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what is the smallest possible integer d for which 2009 + d is a multiple of 11?   

 

Obviously, the question should have said "smallest positive integer" since 

if negative numbers were allowed, there would be no answer because you

could just keep adding that negative number over and over forever. 

 

Divide 11 into 2009. 

 

You'll get 182 with a remainder of 7. 

 

Note that you need to add 4 to take that 7 up to the divisor 11. 

 

Add that 4 to the 2009 and get 2013 which is an even multiple of 11. 

 

The answer is 4. 

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