Product and Sum
The difference between the product and sum of 2 unknown positive integers, X and Y , is exactly 2018.
Hence, find the positive difference between the 2 unknowns.
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1 solution
You need to specify that X and Y are positive integers. Otherwise, there would be infinitely many solutions.
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Thank you for telling me that, I actually changed my question to unknown positive integers before reading your comment on this!
Note that we could also factor 2 0 1 9 simply as 1 × 2 0 1 9 , giving us X = 2 , Y = 2 0 2 0 and thus Y − X = 2 0 1 8 , but this of course was not one of the given options.
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The sum of 1 and 2019 is 2020, the product of 1 and 2019 is 2019, how is the difference 2018?
I don't understand your logic of 1 and 2019 being the answer.
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That's not what I said. We could have the numbers being 2 and 2 0 2 0 , since 2 × 2 0 2 0 − ( 2 + 2 0 2 0 ) = 2 0 1 8 as required, and the difference between 2 and 2 0 2 0 is 2 0 1 8 . However, of the given options only 6 7 0 is possible.
X + Y + 2018 = X Y ,
X Y - X - Y + 1 = 2019,
( X - 1) ( Y - 1) = 2019 = 3 x 673. So 1 of the unknowns is 4 while the other unknown is 674.
Nevertheless, the positive difference between the 2 unknowns is 674 - 4 = 670
Note that the sum of the 2 unknowns cannot be 2018 more than the product.
X + Y = X Y + 2018,
X Y - X - Y + 1 = - 2017
( X - 1) ( Y - 1) = - 2017
As 0 is not a positive integer, one of the unknowns is definitely negative, so this is obviously wrong, hence there is only 1 solution, that the product is 2018 more than the sum, which is above.