If x and y are integers and xy ≠ 0, what is the value of

Question

If x and y are integers and xy ≠ 0, what is the value of  \frac{x^{-2y}}{y^{2x}} ?

(1) x + y = 0

(2) xy = y/x

shreyast · Answer

Answer A. Only statement 1 is sufficient.

\frac{x^{-2y}}{y^{2x}} = \frac{1}{x^{2y}y^{2x}} = \frac{1}{(x^2)^y(y^2)^x}

From statement 1. y = -x, therefore, substituting y by -x, and  y^2  by  x^2 
 = \frac{1}{x^{-2x}x^{2x}}

= \frac{1}{x^{-2x+2x}}

= \frac{1}{x^{0}}

= 1

Statement 2 leads to
 y(x-\frac{1}{x}) = 0

Therefore,  x = \frac{1}{x} . Since it's already given in question that xy is not equal to 0; therefore y can not be 0.
Therefore, x=1 or x = -1, with y unknown.
So our expression's value still depends on value of y, which we don't know. Hence Statement 2 is not sufficient.

Lucky2783 · Answer

(1) x + y = 0
 x=-y if we substitute x into above equation,we will get the 
 
  \frac{x^{-2y}}{y^{2x}}  =1

(2) xy = y/x
 y=0 or x=+- 1 ; y cannot be 0 so X=+- 1 . we do not know about Y. NS.

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: powersinafraction_text.png FAQ: How do we choose what numbers to plug in to test statement 2? The second statement tells us that xy = y/x, which means we can't just pick any numbers. If, for example, x=2, then the statement wouldn't be possible (and remember that's not how data sufficiency works—all statements must be mathematically possible, sufficient or not). That is, any 2y≠y/2, unless y=0. But we know that y≠0 by the statement xy≠0 at the beginning of the question, so that's not allowed. So let's rephrase this: we need a value of x that gives us the same result whether we multiply or divide by x. The only possibilities are 1 and -1. So we plug in x=1, then try a couple different values of y, and find that the results are insufficient, as shown in the video above.

rahulsehgal · Answer

If x and y are integers and xy ≠ 0, what is the value of  \frac{x^{-2y}}{y^{2x}} ?

So let's rephrase this: we need a value of  x  that gives us the same result whether we multiply or divide by x. The only possibilities are 1 and -1.

I believe the above text should say - we need a value of  y  (and not x) that gives us the same result whether we multiply or divide by x. The only possibilities are 1 and -1.

Princ · Answer

If  x  and  y  are integers and  xy
eq{0} , what is the value of  \frac{x^{-2y}}{y^{2x}} ?

x+y =0 
   xy=\frac{y}{x}

GMATBusters · Answer

St1) 
x+y = 0
or, x = -y
x^(-2y)/y^(2x) = (-y)^(-2y)/y^(-2y) = y^(-2y)/y^(-2y) =1
 Sufficient.

St2) xy = y/x
or,  x^2 *y-y =0
or, y( x^2 -1) = 0
or, y =0, or x = +/- 1
Now as xy is not equal to 0, y is not equal to 0.
x = +/- 1, value of y is not known.
hence we can not find the value of given expression.
 Not sufficient.

Answer A

Bunuel · Answer

Merging topics. Please check the discussion above.

bumpbot · Answer

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If x and y are integers and xy ≠ 0, what is the value of

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