If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = : Problem Solving (PS)

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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =

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Joined: 02 Sep 2009

Posts: 60647

If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]

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13 May 2016, 04:54

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Question Stats:

75% (00:55) correct

25% (01:09) wrong

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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

Spoiler: OA

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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]

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Updated on: 13 May 2016, 06:47

X = √5 and Y also =√5
Applying the function (√5+√5)^2 - (√5-√5)^2 = (2√5)^2 - 0 = 4 x 5 = 20. Answer is E.

Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√5 and y = √5 you get the answer 20.

Originally posted by Senthil7 on 13 May 2016, 06:43.
Last edited by Senthil7 on 13 May 2016, 06:47, edited 1 time in total.

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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]

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Updated on: 13 May 2016, 06:48

Bunuel wrote:

If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =

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

Hi
if x ¤ y = (x + y)^2 - (x - y)^2 then √5 ¤ √5 = (√5+√5)^2 - (√5-√5)^2
let solve the equation:
\(√5 ¤ √5 = (√5+√5)^2 - (√5-√5)^2\)
\(=>√5 ¤ √5 = (√5+√5)^2\)
\(=>√5 ¤ √5 = (√5)^2 + 2 * √5 * √5 +(√5)^2\)
\(=>√5 ¤ √5 = 5 + 2 * 5 + 5\)
\(=>√5 ¤ √5 = 5+10+5\)
\(=>√5 ¤ √5 = 10+10\)
\(=>√5 ¤ √5 = 20\)

=> answer is E (20)

Originally posted by HungNguyen on 13 May 2016, 06:46.
Last edited by HungNguyen on 13 May 2016, 06:48, edited 1 time in total.

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Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]

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13 May 2016, 06:47

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

√5 ¤ √5 = 4*5 = 20

OA : E

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Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]

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26 Aug 2016, 11:39

Top Contributor

Bunuel wrote:

If x ¤ y = (x + y)² - (x - y)². Then √5 ¤ √5 =

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

This is a great questions that typifies what I love about most GMAT 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 Then √5 ¤ √5 = [#permalink]

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26 Jul 2017, 09:35

More than anything - Here it pays to first understand what the function actually does.

x ¤ y simply means - \((Sum\ of\ x \ and \ y)^2 - (difference \ of \ x \ and \ y)^2\)

Given \(x=y=\sqrt{5}\).

Therefore (Sum of x and y) = \(2\sqrt{2}\). (Difference of x and y) = 0

WIth Minimum calculation required answer = \((2\sqrt{5})^2 = 20\).

Answer choice E

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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]

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11 Apr 2019, 05:26

\(If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =\)

Another way to simplify is to realize that this is a difference of squares pattern. Really, it's a difference of two terms pattern if I can call it that.

x^2-y^2=(x+y)(x-y)

So, you can spell it out but if you realize, the first terms are positive when factoring, and the second set of terms has just one negative. You'll really end up with \((2*\sqrt{5})\) \((2*\sqrt{5})\)