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03 Mar 2019, 14:28
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Difficulty:
55%
(hard)
Question Stats:
62% (01:54) correct
38%
(02:52)
wrong
based on 39
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GMATH practice exercise (Quant Class 3)
When defined, the expression \(\,{{{x^2} - {y^2}} \over {xy}} - {{xy - {y^2}} \over {xy - {x^2}}}\,\) is equal to:
\(\eqalign{\\
& \left( A \right)\,\,x{y^{ - 1}} \cr \\
& \left( B \right)\,\left( {{x^2} - 2{y^2}} \right){\left( {xy} \right)^{ - 1}} \cr \\
& \left( C \right)\,\,{x^2} \cr \\
& \left( D \right)\,\,x - 2y \cr \\
& \left( E \right)\,\,x + 2y \cr}\)
When defined, the expression \(\,{{{x^2} - {y^2}} \over {xy}} - {{xy - {y^2}} \over {xy - {x^2}}}\,\) is equal to:
\(\eqalign{\\
& \left( A \right)\,\,x{y^{ - 1}} \cr \\
& \left( B \right)\,\left( {{x^2} - 2{y^2}} \right){\left( {xy} \right)^{ - 1}} \cr \\
& \left( C \right)\,\,{x^2} \cr \\
& \left( D \right)\,\,x - 2y \cr \\
& \left( E \right)\,\,x + 2y \cr}\)
03 Mar 2019, 16:02
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Holy algebraic nightmare, Batman! 
Just kidding!
But for real, the GMAT isn't likely to force you to do this level of algebraic manipulation. My advice to students if they see something that is even 50% as complicated as this is to quickly plug in numbers. The GMAT is about flexibility and strategy, not rote calculation.
Just kidding!But for real, the GMAT isn't likely to force you to do this level of algebraic manipulation. My advice to students if they see something that is even 50% as complicated as this is to quickly plug in numbers. The GMAT is about flexibility and strategy, not rote calculation.
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03 Mar 2019, 16:28
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fskilnik
\(? = {{{x^2} - {y^2}} \over {xy}} - {{xy - {y^2}} \over {xy - {x^2}}}\,\,\,\)
\(\frac{{xy - {y^2}}}{{xy - {x^2}}} = \frac{{y\left( {x - y} \right)}}{{x\left( {y - x} \right)}} = \underleftrightarrow {\frac{{ - y\left( {y - x} \right)}}{{x\left( {y - x} \right)}}} = \frac{{ - y}}{x}\)
\(? = \frac{{{x^2} - {y^2}}}{{xy}} + \frac{y}{x} = \underleftrightarrow {\frac{{{x^2} - {y^2}}}{{xy}} + \frac{{y \cdot y}}{{x \cdot y}} = \frac{{{x^2}}}{{xy}}} = \frac{x}{y}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( A \right)\)
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
