jack0997 wrote:Jay@ManhattanReview wrote:jack0997 wrote:If 0 < x < 1 and y > 1, [√{x + y - 2√(xy)} + √{x + y + 2√(xy)}] =
(A) √x
(B) 2√x
(C) √y + √x
(D) √y
(E) 2√y
OA E
An efficient approach for such questions is by plugging in smart values for x and y.
Since we have to deal with √xy, the values chosen for x and y must be such that √xy is not an ugly number.
Say x = 1/4 and y =4. This makes √xy = √(1/4)*4 = √1 = 1. This works.
Just plug-in these values and check which option renders the correct answer.
Hope this helps!
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-Jay
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Thank you, Jay. It was helpful. Could you pl. tell me the algebraic route?
Well, I would not suggest you the Algebraic route; however, for the sake of your interest, here it is.
Say a = √x and b = √y
Thus,
[√{x + y - 2√(xy)} + √{x + y + 2√(xy)}] = [√{a^2 + b^2 - 2ab} + √{a^2 + b^2 + 2ab}]
= {√(a - b)^2} + {√(a + b)^2};
Since y > x, √y > √x, or b > a.
Thus, {√(a - b)^2} + {√(a + b)^2} = (b - a) + (b + a) = 2b = 2√y.
The correct answer:
E
Hope this helps!
Relevant book:
Manhattan Review GMAT Math Essentials Guide
-Jay
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