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DS Is X^2 * Y^4 an integer divisible by 9

Expert replies

by mehravikas » Thu Dec 24, 2009 11:12 pm
Agreed. If you take a decimal then you are unsure whether the product would be divisible by 9.

Thanks Stuart.
Stuart Kovinsky wrote:
Let's simplify the question:

is XY divisible by 9?

(1) x = 9

this might seem sufficient at first glance, but what if y = 1/2? In that case, then xy = 4.5, which is certainly not a multiple of 9.

They key to this question is to realize that Y doesn't have to be an integer; for all integer values of Y we get a "yes" answer (from (1) or (2) alone), but for most non-integer values of Y we get a "no" answer, even after combining the statements.
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