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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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Question Stats: 82% (01:19) correct 18% (01:59) wrong based on 65 sessions

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[Math Revolution GMAT math practice question]

If $$x-2y=4$$, then $$x^2-4xy+4y^2-x+2y=$$?

$$A. 12$$
$$B. 16$$
$$C. 20$$
$$D. 24$$
$$E. 28$$

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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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$$(x-2y)^2 = x^2-4xy+4y^2$$ = 16
$$x^2−4xy+4y^2−x+2y$$ = 16-4 = 12

A is the answer.
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x-2y=4$$, then $$x^2-4xy+4y^2-x+2y=$$?

$$A. 12$$
$$B. 16$$
$$C. 20$$
$$D. 24$$
$$E. 28$$

Let $$x=4$$ and $$y=0$$, with the result that $$x-2y=4$$.
Plugging $$x=4$$ and $$y=0$$ into $$x^2-4xy+4y^2-x+2y=$$, we get:
$$4^2-0+0-4+0=12$$

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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x-2y=4$$, then $$x^2-4xy+4y^2-x+2y=$$?

$$A. 12$$
$$B. 16$$
$$C. 20$$
$$D. 24$$
$$E. 28$$

$$x - 2y = 4\,\,\,\,\,\left( * \right)$$

$$? = \underbrace {{x^2} - 4xy + 4{y^2}}_{{{\left( {x - 2y} \right)}^2}} - x + 2y$$

$$? = {\left( {x - 2y} \right)^2} - \left( {x - 2y} \right)\,\,\,\mathop = \limits_{{\rm{twice}}}^{\left( * \right)} \,\,\,16 - 4 = 12$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x-2y=4$$, then $$x^2-4xy+4y^2-x+2y=$$?

$$A. 12$$
$$B. 16$$
$$C. 20$$
$$D. 24$$
$$E. 28$$

GIVEN: x - 2y = 4
We want to find the value of x² - 4xy + 4y² - x + 2y

We should notice that x² - 4xy + 4y² is equal to (x - 2y)²
We should notice that - x + 2y is equal to -(x - 2y)

We get: x² - 4xy + 4y² - x + 2y = (x - 2y)² - (x - 2y)
Now replace x - 2y with 4 to get: = (x - 2y)² - (x - 2y) = = (4)² - (4)
= 16 - 4
= 12

Cheers,
Brent
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x-2y=4$$, then $$x^2-4xy+4y^2-x+2y=$$?

$$A. 12$$
$$B. 16$$
$$C. 20$$
$$D. 24$$
$$E. 28$$

IMO A

$$x^2-4xy+4y^2-x+2y$$
$$x^2-4xy+4y^2-(x-2y)$$ (a)

x-2y = 4
squaring both sides
$$x^2-4xy+4y^2=16$$

substituting above in (a)
16 - 4
12
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Math Revolution GMAT Instructor V
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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=>

$$x^2-4xy+4y^2-x+2y$$
$$=(x-2y)^2 – (x-2y)$$
$$=4^2 – 4 = 16 – 4 = 12.$$

Therefore, the answer is A.
_________________ Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?   [#permalink] 23 Jan 2019, 01:09
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