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Both x and y are positive integers.

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Carcass
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Both x and y are positive integers. [#permalink] New post   09 Apr 2019, 02:16
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Both x and y are positive integers. If x2+2xy+y2=49 and x2−y2=−7, then y=

A. 2

B. 3

C. 4

D. 5

E. 7
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C
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GreenlightTestPrep
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Re: Both x and y are positive integers. [#permalink] New post   09 Apr 2019, 06:26
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Carcass wrote:
Both x and y are positive integers. If x2+2xy+y2=49 and x2−y2=−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

Answer: C

Cheers,
Brent
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Re: Both x and y are positive integers. [#permalink] New post   22 Dec 2024, 11:28
Hello from the GRE Prep Club BumpBot!

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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Re: Both x and y are positive integers. [#permalink]
22 Dec 2024, 11:28
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