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Is x^2+y^2 divisible by 5? 1). When x-y is divided by 5, the

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Is x^2+y^2 divisible by 5? 1). When x-y is divided by 5, the [#permalink] New post 10 Aug 2007, 10:53
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Is x^2+y^2 divisible by 5?
1). When x-y is divided by 5, the remainder is 1
2). When x+y is divided by 5, the remainder is 3
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Joined: 28 Dec 2004
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 [#permalink] New post 10 Aug 2007, 12:43
I get C too..here is why...

stem: x^2 + y^2 =5M ?

1) x-y=5M +1

well..(x-y)^2=x^2+y^2-2xy=5M=1 as you can see..we dont know if 2xy is causing the remainder 1 or if its x^2+y^2?? Insuff

2) x+y=5M+3

then (x+y)^2 will also give a remainder of 3...

x^2+y^2+2xy= again same reason as above..Insuff

togehter... 2xy cancel..

we have now X^2+y^2; the remainder is 4...

C it is..
  [#permalink] 10 Aug 2007, 12:43
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