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If x + 2y = a and x – 2y = b, which of the following express

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Founder
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If x + 2y = a and x – 2y = b, which of the following express [#permalink] New post 24 Jan 2019, 06:52
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Question Stats:

75% (02:05) correct 25% (01:32) wrong based on 32 sessions
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. \(\frac{a^2-b^2}{8}\)
[Reveal] Spoiler: OA

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Re: If x + 2y = a and x – 2y = b, which of the following express [#permalink] New post 24 Jan 2019, 07:47
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elimination is the best way to solve it,
options (b) and (c) is eliminated as they have solution only in terms of x, not xy which the question is about. Thus they are eliminated
for last 2 option, evaluate a^2-b^2 which is 8xy. Therefore, option d is the correct answer
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Re: If x + 2y = a and x – 2y = b, which of the following express [#permalink] New post 26 Jul 2020, 11:05
Expert's post
\(x=a-2y\) and \(x=b+2y\)

\(a-2y=b+2y\)

\(a-b=4y\)

\(y=\frac{a-b}{4}\)

\(2y=a-x\)

\(2y=x-b\)

\(a-x=x-b\)

\(x=\frac{a+b}{2}\)

\(x \times y\)


\(\frac{a-b}{4} \times \frac{a+b}{2}\)

\(\frac{(a-b)^2}{8}\)

Answer is E
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Re: If x + 2y = a and x – 2y = b, which of the following express   [#permalink] 26 Jul 2020, 11:05
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If x + 2y = a and x – 2y = b, which of the following express

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