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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: 53768
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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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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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:
$$√5 ¤ √5 = (√5+√5)^2 - (√5-√5)^2$$
$$=>√5 ¤ √5 = (√5+√5)^2$$
$$=>√5 ¤ √5 = (√5)^2 + 2 * √5 * √5 +(√5)^2$$
$$=>√5 ¤ √5 = 5 + 2 * 5 + 5$$
$$=>√5 ¤ √5 = 5+10+5$$
$$=>√5 ¤ √5 = 10+10$$
$$=>√5 ¤ √5 = 20$$

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 = $$(2\sqrt{5})^2 = 20$$.

Aside Moderators: Do you think it will be nice'er' if the stem is made math friendly?
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Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

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04 Mar 2019, 07:59
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Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =   [#permalink] 04 Mar 2019, 07:59
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