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by goalevan » Fri Jul 01, 2011 5:36 pm
This question can be written algebraically as follows:

dividend/divisor = quotient + remainder/divisor, or dividend = divisor * quotient + remainder

Where k is some integer quotient, the question is: 15/y = k + (y - 3)/y, or 15 = k*y + (y - 3).
Rearranging, we have 15 = y(k+1) - 3, or:

18/y = k+1.

We know that k is some integer, thus k+1 is also an integer. In order for this to be true, 18 must be divisible by y. In other words, y must be a factor of 18.

The answer ignoring any constraints would simply be all factors of 18 = 2^1 * 3^2, or 1, 2, 3, 6, 9, and 18.

But, a remainder cannot be less than 0, and cannot be greater than or equal to the divisor. Therefore (y-3) >= 0, or y >= 3, and (y-3) <= y, or 0 <= 3. The second constraint is always true, but the first eliminates the first two factors of 18, 1 and 2.

The answer is thus 3, 6, 9, 18.
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by chaitanya.mehrotra » Sat Jul 02, 2011 1:30 am
Thanks Goalevan
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