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# Both x and y are positive integers.

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Kudos [?]: 1371 [0], given: 6384

Both x and y are positive integers. [#permalink]  09 Apr 2019, 02:16
Expert's post
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Question Stats:

83% (01:45) correct 16% (00:21) wrong based on 6 sessions
Both x and y are positive integers. If $$x^2 + 2xy + y^2 = 49$$ and x$$^2 − y^2 = − 7$$, then $$y =$$

A. 2

B. 3

C. 4

D. 5

E. 7
[Reveal] Spoiler: OA

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GRE Instructor
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Kudos [?]: 1841 [1] , given: 9

Re: Both x and y are positive integers. [#permalink]  09 Apr 2019, 06:26
1
KUDOS
Expert's post
Carcass wrote:
Both x and y are positive integers. If $$x^2 + 2xy + y^2 = 49$$ and x$$^2 − y^2 = − 7$$, then $$y =$$

A. 2

B. 3

C. 4

D. 5

E. 7

GIVEN: x² + 2xy + y² = 49
Factor to get: (x + y)² = 49

So, EITHER x + y = 7 OR x + y = -7
Since we're told that x and y are POSITIVE, we can be certain that x + y = 7

GIVEN: x² - y² = −7
Factor to get: (x + y)(x - y) = -7
Replace x + y with 7 to get: (7)(x - y) = -7
So, we know that x - y = -1

We now have two linear equations:
x + y = 7
x - y = -1

Subtract the BOTTOM equation from the TOP equation to get: 2y = 8
Solve: y = 8/2 = 4

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: Both x and y are positive integers.   [#permalink] 09 Apr 2019, 06:26
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