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If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =
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Updated on: 25 May 2020, 11:54
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Kudos
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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 _________________
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =
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Updated on: 13 May 2016, 05:47
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, 05:43.
Last edited by Senthil7 on 13 May 2016, 05:47, edited 1 time in total.
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =
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11 Apr 2019, 04:26
\(If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =\)
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 \((2*\sqrt{5})\)\((2*\sqrt{5})\)
gmatclubot
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = [#permalink]
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