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

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Updated on: 04 Dec 2018, 06:02
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Project DS Butler: Day 28: Data Sufficiency (DS55)

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

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Originally posted by GMATBusters on 04 Dec 2018, 05:57.
Last edited by Bunuel on 04 Dec 2018, 06:02, edited 1 time in total.
Renamed the topic and edited the question.
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If xy ≠ 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)  [#permalink]

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Updated on: 09 Apr 2020, 14:08
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gmatbusters wrote:
If $$xy\neq{0}$$, what is the value of $$\frac{(x^4y^2- (xy)^2)}{(x^3y^2)}$$

(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

VIDEO ON REPHRASING THE TARGET QUESTION

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Originally posted by BrentGMATPrepNow on 04 Dec 2018, 06:59.
Last edited by BrentGMATPrepNow on 09 Apr 2020, 14:08, edited 1 time in total.
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If xy ≠ 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)  [#permalink]

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04 Dec 2018, 18:51
gmatbusters wrote:

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

$$x,y\,\, \ne 0$$

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

$$\left( 1 \right)\,\,x = 2\,\,\,\, \Rightarrow \,\,\,\,?\,\,\,{\rm{unique}}$$

$$\left( 2 \right)\,\,y = 8\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,? = 0 \hfill \cr \,{\rm{Take}}\,\,x = 2\,\,\,\, \Rightarrow \,\,\,? \ne 0 \hfill \cr} \right.$$

The correct answer is therefore (A).

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

Regards,
Fabio.
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Re: If xy ≠ 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)  [#permalink]

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05 Dec 2018, 01:40
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 $$x$$...
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Re: If xy ≠ 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)  [#permalink]

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06 Dec 2018, 05:39
T1101 wrote:
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 $$x$$...

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
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Re: If xy ≠ 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)  [#permalink]

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06 Dec 2018, 06:33
gota900 wrote:
T1101 wrote:
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 $$x$$...

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

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

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24 May 2020, 05:41
GMATBusters wrote:

Project DS Butler: Day 28: Data Sufficiency (DS55)

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

Asked: If $$xy\neq{0}$$, 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
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If xy ≠ 0, what is the value of (x^4*y^2- (xy)^2)/(x^3*y^2)   [#permalink] 24 May 2020, 05:41