Carcass wrote:
If \(x ¤ y = (x + y)^2 - (x - y)^2\). Then \(√5 ¤ √5 =\)
A. 0
B. 5
C. 10
D. 15
E. 20
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math BookThis is a great questions that typifies what I love about most GRE 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