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If x + y = 7 and x – y = 3, then x^2 - y^2 =

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Carcass
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If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post   22 Feb 2021, 09:56
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If x+y=7 and x – y = 3, then x^2 - y^2 =

A. -4
B. 4
C. 10
D. 21
E. 40


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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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D
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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post   22 Feb 2021, 10:31
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Carcass wrote:
If x + y = 7 and x – y = 3, then x^2 - y^2 =

A. -4
B. 4
C. 10
D. 21
E. 40


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


APPROACH #1: Factor the difference of squares
Key property: (a^2 - b^2)=(a+b)(a-b)

So, (x^2 - y^2)=(x+y)(x-y)
=(7)(3)
=21

Answer: D

APPROACH #2: Solve the system of equations
Given:
x + y = 7
x – y = 3
Add the two equations to get: 2x = 10, which means x = 5
If x = 5, we can plug that value into either equation, to conclude that y = 2

If x = 5 and y = 2, then x^2 - y^2 = 5^2 - 2^2 = 25 - 4 = 21

Answer: D

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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post   27 Apr 2021, 04:03
I am really enjoying honing my technique of finding the hidden properties (difference of squares in this case) in these questions. Great practice for identifying the trick, and becoming easier!
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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post   28 Apr 2021, 01:50
We solve the equations together, add them up, and then it's a matter of technique.
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Re: If x + y = 7 and x – y = 3, then x^2 - y^2 = [#permalink] New post   28 Apr 2021, 04:53
x=5 and y=2


Answer - D
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Re: If x + y = 7 and x y = 3, then x^2 - y^2 = [#permalink] New post   19 Jan 2024, 12:32
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