If 0 < x < 1 and y > 1

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!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

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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!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

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
_________________
Manhattan Review GMAT Prep

Locations: New York | Mumbai | Ho Chi Minh City | Budapest | and many more...

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