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If x ¤ y = (x + y)^2 - (x - y)^2.

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Carcass
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If x ¤ y = (x + y)^2 - (x - y)^2. [#permalink] New post   15 Mar 2021, 10:33
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If \(x ¤ y = (x + y)^2 - (x - y)^2\). Then \(√5 ¤ √5 =\)

A. 0
B. 5
C. 10
D. 15
E. 20


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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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E
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GreenlightTestPrep
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If x ¤ y = (x + y)^2 - (x - y)^2. [#permalink] New post   15 Mar 2021, 10:36
Carcass wrote:
If \(x ¤ y = (x + y)^2 - (x - y)^2\). Then \(√5 ¤ √5 =\)

A. 0
B. 5
C. 10
D. 15
E. 20


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


This is a great questions that typifies what I love about most GRE math questions: they can almost always be solved in more than 1 way.

One option is to plug the values into the "recipe" and get...
√5 ¤ √5 = (√5 + √5)² - (√5 - √5)²
= (2√5)² - (0)²
= (2√5)(2√5)
= 4√25
= 20
= D

Another option is to simplify the recipe before plugging in the values
x ¤ y = (x + y)² - (x - y)²
= (x² + 2xy + y²) - (x² - 2xy + y²)
= 4xy
So, x ¤ y = 4xy
NOW plug in the values to get....
√5 ¤ √5 = 4(√5)(√5)
= 4√25
= 20
= D
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Re: If x ¤ y = (x + y)^2 - (x - y)^2. [#permalink] New post   15 Mar 2021, 23:23
Carcass wrote:
If \(x ¤ y = (x + y)^2 - (x - y)^2\). Then \(√5 ¤ √5 =\)

A. 0
B. 5
C. 10
D. 15
E. 20


Use \(a^2 - b^2 = (a + b)(a - b)\)

\(x ¤ y = (x + y)^2 - (x - y)^2 = (x + y + x - y)(x + y - x + y) = (2x)(2y) = 4xy\)

\(√5 ¤ √5 = 4(\sqrt{5})(\sqrt{5}) = 4(5) = 20\)

Hence, option E
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gmatclubot
Re: If x ¤ y = (x + y)^2 - (x - y)^2. [#permalink]
15 Mar 2021, 23:23
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