If xy 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)

Question

If  xy
eq{0} , what is the value of  \frac{(x^4*y^2- (xy)^2)}{(x^3*y^2)}

(1) x = 2
(2) y = 8

BrentGMATPrepNow · Answer

Target question :    What is the value of  \frac{(x^4y^2- (xy)^2)}{(x^3y^2)}   
This is a good candidate for  rephrasing the target question.

\frac{(x^4y^2- (xy)^2)}{(x^3y^2)} = \frac{(x^4y^2- x^2y^2)}{(x^3y^2)}

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

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

REPHRASED target question :    What is the value of  \frac{x^2-1}{x}   ?

Aside: there’s a video below with tips on rephrasing the target question

Statement 1 : x = 2  
Since the REPHRASED target question involves only the value of x, we can simply plug x = 2 into the expression .
We get:  \frac{x^2-1}{x}=\frac{2^2-1}{2}=\frac{3}{2} 
Since we can answer the  REPHRASED target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : y = 8  
Since the REPHRASED target question involves only the value of x, the value of y is of no use to us. 
Statement 2 is NOT SUFFICIENT

Answer: A

VIDEO ON REPHRASING THE TARGET QUESTION
 https://www.youtube.com/watch?v=MyG1K3ee69w

fskilnik · Answer

x,y\,\, 
e 0

? = {{{x^2} \cdot {y^2} \cdot \left( {{x^2} - 1} ight)} \over {{x^2} \cdot {y^2} \cdot x}} = {{{x^2} - 1} \over x}

\left( 1 ight)\,\,x = 2\,\,\,\, \Rightarrow \,\,\,\,?\,\,\,{m{unique}}

\left( 2 ight)\,\,y = 8\,\,\left\{ \matrix{
 \,{m{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,? = 0 \hfill \cr 
 \,{m{Take}}\,\,x = 2\,\,\,\, \Rightarrow \,\,\,? 
e 0 \hfill \cr} ight.

The correct answer is therefore (A).

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

T1101 · Answer

IMO A

But I rephrased the question stem in a slightly different way:

\frac{(x^4*y^2- (xy)^2)}{(x^3*y^2)}  can be split in to fractions:  \frac{x^4*y^2}{x^3*y^2}-\frac{(xy)^2}{x^3*y^2}

Simplify further:  x-\frac{x^2*y^2}{x^3*y^2}   =   x-\frac{1}{x}

We only need the value of  x ...

gota900 · Answer

It seems to me that you went for the wrong approach here mate. It turns out that you can answer the question correctly by using your method, but this is just lucky here. You missed that the term in the numerator is in brackets, which is why your approach has no applicability here.

Best, LB

T1101 · Answer

Why does it matter if the term in the numerator is in brackets? I can still split it since the denominator does not involve subraction or addition? Can you eloborate please?

Furhtermore I can reduce \frac{(x^2-1)}{x}  into  \frac{x^2}{x}-\frac{1}{x}  -->  x-\frac{1}{x} , which is the same as with the oterh approach...

Kindly correct me if I am wrong

Kinshook · Answer

Asked: If  xy
eq{0} , what is the value of  \frac{(x^4*y^2- (xy)^2)}{(x^3*y^2)} 
 \frac{(x^4*y^2- (xy)^2)}{(x^3*y^2)} = x - \frac{1}{x}

(1) x = 2
 \frac{(x^4*y^2- (xy)^2)}{(x^3*y^2)} = x - \frac{1}{x} = 2 - \frac{1}{2} = 1.5 
SUFFICIENT

(2) y = 8
 \frac{(x^4*y^2- (xy)^2)}{(x^3*y^2)} = x - \frac{1}{x}   is independent of y
NOT SUFFICIENT

IMO A

KanikaJain · Answer

If xy≠0, what is the value of (x^4∗y^2)−(xy)^2)/(x^3∗y^2)

(1) x = 2
(2) y = 8

Solving the equation, (x^2-1)/x remains. Thus only x =2 gives the value - thus A

If xy 0, what is the value of (x^4y^2- (xy)^2)/(x^3y^2)

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