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If xy 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)
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Updated on: 08 Feb 2024, 01:14
Updated on: 08 Feb 2024, 01:14
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If \(xy\neq{0}\), what is the value of \(\frac{(x^4*y^2- (xy)^2)}{(x^3*y^2)}\)
(1) x = 2
(2) y = 8
(1) x = 2
(2) y = 8
Originally posted by GMATBusters on 04 Dec 2018, 06:57.
Last edited by Bunuel on 08 Feb 2024, 01:14, edited 2 times in total.
Last edited by Bunuel on 08 Feb 2024, 01:14, edited 2 times in total.
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Re: If xy 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)
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Updated on: 09 Apr 2020, 15:08
Updated on: 09 Apr 2020, 15:08
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gmatbusters
If \(xy\neq{0}\), what is the value of \(\frac{(x^4y^2- (xy)^2)}{(x^3y^2)}\)
(1) x = 2
(2) y = 8
(1) x = 2
(2) y = 8
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
Originally posted by BrentGMATPrepNow on 04 Dec 2018, 07:59.
Last edited by BrentGMATPrepNow on 09 Apr 2020, 15:08, edited 1 time in total.
Last edited by BrentGMATPrepNow on 09 Apr 2020, 15:08, edited 1 time in total.
Re: If xy 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)
[#permalink]
04 Dec 2018, 19:51
04 Dec 2018, 19:51
Expert Reply
gmatbusters
If \(xy\neq{0}\), what is the value of \(\frac{(x^4*y^2- (xy)^2)}{(x^3*y^2)}\)
(1) x = 2
(2) y = 8
\(? = {{{x^2} \cdot {y^2} \cdot \left( {{x^2} - 1} \right)} \over {{x^2} \cdot {y^2} \cdot x}} = {{{x^2} - 1} \over x}\)
\(\left( 1 \right)\,\,x = 2\,\,\,\, \Rightarrow \,\,\,\,?\,\,\,{\rm{unique}}\)
\(\left( 2 \right)\,\,y = 8\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,? = 0 \hfill \cr \\
\,{\rm{Take}}\,\,x = 2\,\,\,\, \Rightarrow \,\,\,? \ne 0 \hfill \cr} \right.\)
The correct answer is therefore (A).
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
