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If x and y are different integers and x ^2 = x * y, which of

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Director
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If x and y are different integers and x ^2 = x * y, which of [#permalink] New post 08 Jun 2008, 18:52
If x and y are different integers and x ^2 = x * y, which of the following must be true?

x =0
y =0
x = -y

I only
II only
III only
I and II only
I II III

Approach. x * x = x * y =
x = y

The only value that would make x and y distinct is III only.
say y = 1, x = -1

What do you guys think?
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Re: value of x [#permalink] New post 08 Jun 2008, 19:09
alimad wrote:
If x and y are different integers and x ^2 = x * y, which of the following must be true?

x =0
y =0
x = -y

I only
II only
III only
I and II only
I II III

Approach. x * x = x * y =
x = y

The only value that would make x and y distinct is III only.
say y = 1, x = -1

What do you guys think?


But be careful X and Y are different interger. So II can not be true. I think only I is true.
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Re: value of x [#permalink] New post 08 Jun 2008, 19:16
i'm sorry can you elaborate, why is III not the answer since x and y are different?
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Re: value of x [#permalink] New post 08 Jun 2008, 19:22
alimad wrote:
If x and y are different integers and x ^2 = x * y, which of the following must be true?

x =0
y =0
x = -y

I only
II only
III only
I and II only
I II III

Approach. x * x = x * y =
x = y

The only value that would make x and y distinct is III only.
say y = 1, x = -1

What do you guys think?


x ^2 = x * y
=> x(x-y) = 0
if x NE y, then x must be zero.
Ans A.
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Re: value of x [#permalink] New post 08 Jun 2008, 19:26
alimad wrote:
i'm sorry can you elaborate, why is III not the answer since x and y are different?


The only value that would make x and y distinct is III only.
say y = 1, x = -1

I used your quote. If y=1 and x=-1 the equation will not hold true any more remember x^2=x*y?
If you plug this in (-1)^2 =1 but (-1)*1=-1 the two sides will not equal. Make sense?
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Re: value of x [#permalink] New post 08 Jun 2008, 22:58
I go with A. x^2=xy
so x^2-xy=0
x(x-y)=0
Either x=0 or x=y
But x and y are distinct integers so x must be zero
Re: value of x   [#permalink] 08 Jun 2008, 22:58
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