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# If x+2y = a and x-2y=b, which of the following expressions i

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Intern
Joined: 06 Apr 2012
Posts: 30
If x+2y = a and x-2y=b, which of the following expressions i  [#permalink]

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25 Sep 2013, 10:58
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81% (01:28) correct 19% (02:21) wrong based on 114 sessions

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If x+2y = a and x-2y=b, which of the following expressions is equal to xy?

A) $$ab$$

B) $$\frac{a+b}{2}$$

C) $$\frac{a-b}{2}$$

D) $$\frac{a^2-b^2}{4}$$

E) $$\frac{a^2-b^2}{8}$$

Source: Barron's.

Similar problem in OG,#227, I thought I could solve those easily... Though it is not too hard when picking numbers, I can't get to the answer algebraically. Would appreciate the help.
Math Expert
Joined: 02 Sep 2009
Posts: 50009
Re: If x+2y = a and x-2y=b, which of the following expressions i  [#permalink]

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25 Sep 2013, 11:05
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ikokurin wrote:
If x+2y = a and x-2y=b, which of the following expressions is equal to xy?

A) $$ab$$

B) $$\frac{a+b}{2}$$

C) $$\frac{a-b}{2}$$

D) $$\frac{a^2-b^2}{4}$$

E) $$\frac{a^2-b^2}{8}$$

Source: Barron's.

Similar problem in OG,#227, I thought I could solve those easily... Though it is not too hard when picking numbers, I can't get to the answer algebraically. Would appreciate the help.

Sum the equations: $$2x=a+b$$.
Subtract the equations: $$4y=a-b$$.

Multiply: $$8xy=a^2-b^2$$ --> $$xy=\frac{a^2-b^2}{8}$$.

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Intern
Joined: 14 Feb 2012
Posts: 22
Re: If x+2y = a and x-2y=b, which of the following expressions i  [#permalink]

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22 Oct 2013, 06:34
Bunuel wrote:
ikokurin wrote:
If x+2y = a and x-2y=b, which of the following expressions is equal to xy?

A) $$ab$$

B) $$\frac{a+b}{2}$$

C) $$\frac{a-b}{2}$$

D) $$\frac{a^2-b^2}{4}$$

E) $$\frac{a^2-b^2}{8}$$

Source: Barron's.

Similar problem in OG,#227, I thought I could solve those easily... Though it is not too hard when picking numbers, I can't get to the answer algebraically. Would appreciate the help.

Sum the equations: $$2x=a+b$$.
Subtract the equations: $$4y=a-b$$.

Multiply: $$8xy=a^2-b^2$$ --> $$xy=\frac{a^2-b^2}{8}$$.

How do you create the second step? Im sorry, but I don't really get the second step.
All the rest is clear.
Math Expert
Joined: 02 Sep 2009
Posts: 50009
Re: If x+2y = a and x-2y=b, which of the following expressions i  [#permalink]

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22 Oct 2013, 08:56
waltiebikkiebal wrote:
Bunuel wrote:
ikokurin wrote:
If x+2y = a and x-2y=b, which of the following expressions is equal to xy?

A) $$ab$$

B) $$\frac{a+b}{2}$$

C) $$\frac{a-b}{2}$$

D) $$\frac{a^2-b^2}{4}$$

E) $$\frac{a^2-b^2}{8}$$

Source: Barron's.

Similar problem in OG,#227, I thought I could solve those easily... Though it is not too hard when picking numbers, I can't get to the answer algebraically. Would appreciate the help.

Sum the equations: $$2x=a+b$$.
Subtract the equations: $$4y=a-b$$.

Multiply: $$8xy=a^2-b^2$$ --> $$xy=\frac{a^2-b^2}{8}$$.

How do you create the second step? Im sorry, but I don't really get the second step.
All the rest is clear.

Subtract $$x-2y=b$$ from $$x+2y = a$$:

$$(x+2y)-(x-2y) = a-b$$ --> $$4y=a-b$$.

Hope it's clear.
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Joined: 09 Sep 2013
Posts: 8510
Re: If x+2y = a and x-2y=b, which of the following expressions i  [#permalink]

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03 Mar 2017, 21:31
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Re: If x+2y = a and x-2y=b, which of the following expressions i &nbs [#permalink] 03 Mar 2017, 21:31
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# If x+2y = a and x-2y=b, which of the following expressions i

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