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If x - y = 1/2 and x2 - y2 = 3, what is the value of x + y?

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GMAT Club Legend
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If x - y = 1/2 and x2 - y2 = 3, what is the value of x + y? [#permalink] New post 19 May 2018, 16:16
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100% (00:31) correct 0% (00:00) wrong based on 6 sessions
If \(x - y = \frac{1}{2}\) and \(x^2 - y^2 = 3\), what is the value of x + y?

[Reveal] Spoiler: OA
6

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Intern
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Re: If x - y = 1/2 and x2 - y2 = 3, what is the value of x + y? [#permalink] New post 26 May 2018, 13:04
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Good question -
x - y = 1/2
x^2 - y^2 = 3
from equation 1 we get x = y+1/2
put in the second equation to get x = 13/4 . Then calculate y , y = 11/4 .
(13+11)/4 = 6.

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Re: If x - y = 1/2 and x2 - y2 = 3, what is the value of x + y? [#permalink] New post 26 May 2018, 16:28
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sandy wrote:
If \(x - y = \frac{1}{2}\) and \(x^2 - y^2 = 3\), what is the value of x + y?

[Reveal] Spoiler: OA
6


We can also solve this by first recognizing that x² - y² is a difference of squares
We know that x² - y² = (x + y)(x - y)

Given: x² - y² = 3
Factor to get: (x + y)(x - y) = 3

We're also told that x - y = 1/2

So, we can now say: (x + y)(1/2) = 3
From this, we know that x + y = 6

Answer: 6

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: If x - y = 1/2 and x2 - y2 = 3, what is the value of x + y?   [#permalink] 26 May 2018, 16:28
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