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13 May 2016, 04:54
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (00:56) correct
22%
(01:09)
wrong
based on 274
sessions
History
Date
Time
Result
Not Attempted Yet
If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 =
A. 0
B. 5
C. 10
D. 15
E. 20
A. 0
B. 5
C. 10
D. 15
E. 20
Updated on: 25 May 2020, 12:54
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.
Last edited by BrentGMATPrepNow on 25 May 2020, 12:54, edited 1 time in total.
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Bunuel
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
General Discussion
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.
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.
