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

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by Max@Math Revolution » Sun Jan 20, 2019 11:59 pm
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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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by GMATGuruNY » Mon Jan 21, 2019 3:28 am
Max@Math Revolution 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 x² - 4xy + 4y² - x + 2y, we get:
4² - 0 + 0 - 4 + 0 = 12.

The correct answer is A.
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by fskilnik@GMATH » Mon Jan 21, 2019 4:25 am
Max@Math Revolution 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.

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by Brent@GMATPrepNow » Mon Jan 21, 2019 6:44 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If x - 2y = 4, then x² - 4xy + 4y² - 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

Answer: A

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by Max@Math Revolution » Tue Jan 22, 2019 11:53 pm
=>

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

Therefore, the answer is A.
Answer: A
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