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Math Expert V
Joined: 02 Sep 2009
Posts: 61252
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

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2 00:00

Difficulty:   15% (low)

Question Stats: 75% (00:55) correct 25% (01:09) wrong based on 184 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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GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4320
Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

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1
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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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

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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, 05:43.
Last edited by Senthil7 on 13 May 2016, 05:47, edited 1 time in total.
Intern  Joined: 07 May 2016
Posts: 25
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

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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

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, 05:46.
Last edited by HungNguyen on 13 May 2016, 05:48, 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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(x + y)^2 - (x - y)^2 = 4xy

√5 ¤ √5 = 4*5 = 20

OA : E
Manager  G
Joined: 12 Jun 2016
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Re: If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

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

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Manager  S
Joined: 15 Jan 2018
Posts: 66
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =  [#permalink]

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

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 $$(2*\sqrt{5})$$ $$(2*\sqrt{5})$$ If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =   [#permalink] 11 Apr 2019, 04:26
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