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If x + y = 7 and x – y = 3, then x^2 - y^2 =
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22 Feb 2021, 09:56
22 Feb 2021, 09:56
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Question Stats:
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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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x + y = 7 and x – y = 3, then x^2 - y^2 =
[#permalink]
22 Feb 2021, 10:31
22 Feb 2021, 10:31
1
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
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
Cheers,
Brent
Re: If x + y = 7 and x – y = 3, then x^2 - y^2 =
[#permalink]
27 Apr 2021, 04:03
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!
