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![If (x + y)/(x y) = (2x + 2y)/[x + 2(xy) + y], what is the ratio](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If (x + y)/(x y) = (2x + 2y)/[x + 2(xy) + y], what is the ratio"){kind=icon}
05 Nov 2014, 08:33
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E
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Difficulty:
65%
(hard)
Question Stats:
63% (02:42) correct
37%
(02:58)
wrong
based on 424
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If \(\frac{\sqrt{x} + \sqrt{y}}{x - y} = \frac{2\sqrt{x} + 2\sqrt{y}}{x + 2\sqrt{xy} + y}\), what is the ratio of x to y ?
A. 1/2
B. 2
C. 4
D. 7
E. 9
A. 1/2
B. 2
C. 4
D. 7
E. 9
09 Nov 2014, 19:54
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\(\frac{\sqrt{x} + \sqrt{y}}{x - y} = \frac{2\sqrt{x} + 2\sqrt{y}}{x + 2\sqrt{xy} + y}\)
\(\frac{\sqrt{x} + \sqrt{y}}{(\sqrt{x} - \sqrt{y})(\sqrt{x} + \sqrt{y})} = \frac{2(\sqrt{x} + \sqrt{y})}{(\sqrt{x} + \sqrt{y})^2}\)
\(\frac{\sqrt{x} + \sqrt{y}}{\sqrt{x} - \sqrt{y}} = 2\)
Using componendo / dividend
\(\frac{2\sqrt{x}}{\sqrt{x} - \sqrt{y}} = \frac{2+1}{1} = 3\) ....................... (1)
\(\frac{2\sqrt{y}}{\sqrt{x} - \sqrt{y}} = \frac{2-1}{1} = 1\) ........................ (2)
Divide (1) by (2)
\(\frac{\sqrt{x}}{\sqrt{y}} = \frac{3}{1}\)
\(\frac{x}{y} = 9\)
Answer = E
\(\frac{\sqrt{x} + \sqrt{y}}{(\sqrt{x} - \sqrt{y})(\sqrt{x} + \sqrt{y})} = \frac{2(\sqrt{x} + \sqrt{y})}{(\sqrt{x} + \sqrt{y})^2}\)
\(\frac{\sqrt{x} + \sqrt{y}}{\sqrt{x} - \sqrt{y}} = 2\)
Using componendo / dividend
\(\frac{2\sqrt{x}}{\sqrt{x} - \sqrt{y}} = \frac{2+1}{1} = 3\) ....................... (1)
\(\frac{2\sqrt{y}}{\sqrt{x} - \sqrt{y}} = \frac{2-1}{1} = 1\) ........................ (2)
Divide (1) by (2)
\(\frac{\sqrt{x}}{\sqrt{y}} = \frac{3}{1}\)
\(\frac{x}{y} = 9\)
Answer = E
11 Nov 2014, 13:23
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(√x + √y)/(x - y) = (2√x + 2√y)/[x + 2√(xy) + y]
taking (√x + √y) common from both the sides, we get
1/(x - y) = 2/[x + 2√(xy) + y]
(Also, x + 2√(xy) + y = (√x + √y)^2)
therefore,
1/(x - y) = 2/(√x + √y)^2
Now (x - y) can also be written as √x^2 - √y^2
therfore,
1/(√x^2 - √y^2) = 2/(√x + √y)^2
1/(√x + √y) (√x - √y) = 2/ (√x + √y) (√x + √y)
1/(√x - √y) = 2/(√x + √y)
2(√x - √y) = (√x + √y)
(2√x - 2√y) = (√x + √y)
√x = 3√y
squaring both the sides,
x=9y
x/y = 9
therefore, the answer is E
Hope it helps
taking (√x + √y) common from both the sides, we get
1/(x - y) = 2/[x + 2√(xy) + y]
(Also, x + 2√(xy) + y = (√x + √y)^2)
therefore,
1/(x - y) = 2/(√x + √y)^2
Now (x - y) can also be written as √x^2 - √y^2
therfore,
1/(√x^2 - √y^2) = 2/(√x + √y)^2
1/(√x + √y) (√x - √y) = 2/ (√x + √y) (√x + √y)
1/(√x - √y) = 2/(√x + √y)
2(√x - √y) = (√x + √y)
(2√x - 2√y) = (√x + √y)
√x = 3√y
squaring both the sides,
x=9y
x/y = 9
therefore, the answer is E
Hope it helps
