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Both x and y are positive integers.
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09 Apr 2019, 02:16
09 Apr 2019, 02:16
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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
A. 2
B. 3
C. 4
D. 5
E. 7
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Both x and y are positive integers.
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09 Apr 2019, 06:26
09 Apr 2019, 06:26
2
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
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
Answer: C
Cheers,
Brent
Re: Both x and y are positive integers.
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26 May 2023, 07:38
26 May 2023, 07:38
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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