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

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Bunuel
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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink] New post   13 May 2016, 04:54
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78% (00:56) correct 22% (01:12) wrong based on 231 sessions
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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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E
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BrentGMATPrepNow
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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink] New post   Updated on: 25 May 2020, 12:54
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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

Originally posted by BrentGMATPrepNow on 26 Aug 2016, 11:39.
Last edited by BrentGMATPrepNow on 25 May 2020, 12:54, edited 1 time in total.
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Senthil7
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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink] New post   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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HungNguyen
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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink] New post   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] New post   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] New post   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

Aside Moderators: Do you think it will be nice'er' if the stem is made math friendly? :)
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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink] New post   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 \((2*\sqrt{5})\) \((2*\sqrt{5})\)
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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
11 Apr 2019, 05:26
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