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# If x,y are non-negative integers , what is the value of

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Manager
Joined: 28 Aug 2006
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If x,y are non-negative integers , what is the value of [#permalink]  21 Jul 2007, 16:11
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If x,y are non-negative integers , what is the value of 3^xy?

1. 5^x = 11^y
2. 3^x = 9^y
Senior Manager
Joined: 14 Jun 2007
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I go for A

Statement I gives us that 5^x = 11^y
.
my initial logic was that any multiple of 5 will end in five and any multiple of 11 will end in 1 so they are never equal. also 5 and 11 are both primes, this is not an elegant way of explaining it.. but they do not share any prime factors... sp no matter what positve/negative power you put on 11 it will never have a five as one its factors and vice versa.. therefore x=y=0 and 3^xy =1

Statement II gives us that 3^x = 9^y this is true when x=y=0, but it is also true when x=4 and y=2. It might be true for other numbers as well i have no idea how to test or prove it.
Intern
Joined: 18 Jul 2007
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it is indeed A.

To evaluate statement 2... 3^x = 9^y
you can rewrite 9^y = (3^2)^y = 3^(2y)
so we get 3^x = 3^(2y) thus x = 2y

if y = 1, x = 2
if y = 2, x = 4 .. etc
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