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X = 0 [#permalink] New post 12 Jan 2004, 15:41
From the below question, if x=o, the answer states that if x=0, and y = 3 clearly satisfy x^2=xy. I was thinking if x=o, y would be 0. Could anyone explain?

If x and y are different integers and x^2=xy, which of the must be true?

I. x = 0
II. y = 0
III. x = -y

a) I only
b) II only
c) III only
d) I an III only
e) I, II, III
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 [#permalink] New post 12 Jan 2004, 15:44
If X is zero, Y can be anything you want it to be.
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 [#permalink] New post 12 Jan 2004, 16:07
x^2 = xy
x^2 - xy = 0
x ( x - y ) = 0
Therefore, for the equation to hold, X HAS to = 0
Y could be anything. Y does not have to be 0. Say Y = 0 but X = 5, then the expression does not equal to 0. say X = -Y and X = 5 then Y = -5. Plug it in the formula to get 5 ( 5 - (-5) ) = 5*10 = 50 and not equal to 0. True that Y = to 0 ONLY IF X is. However, the expression will NOT give you 0 in all scenarios if only Y = 0.
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Paul

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 [#permalink] New post 13 Jan 2004, 02:52
a) 1 only? becoz x has to be 0 but y can be anything
  [#permalink] 13 Jan 2004, 02:52
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