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If x + y = 6t
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23 Feb 2021, 02:04
23 Feb 2021, 02:04
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Question Stats:
73% (01:46) correct
26% (01:42) wrong based on 26 sessions
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If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?
A. 20
B. 30
C. 50
D. 60
E. 90
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 20
B. 30
C. 50
D. 60
E. 90
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: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
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If x + y = 6t
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23 Feb 2021, 06:53
23 Feb 2021, 06:53
1
Carcass wrote:
If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?
A. 20
B. 30
C. 50
D. 60
E. 90
A. 20
B. 30
C. 50
D. 60
E. 90
\(\frac{(x^2 + y^2)}{t^2}\)
\(\frac{(x + y)^2 - 2xy}{t^2}\)
\(\frac{(6t)^2 - (2)(-7t^2)}{t^2}\)
\(\frac{(36t^2 + 14t^2)}{t^2}\)
\(\frac{50t^2}{t^2} = 50\)
Hence, option C
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x + y = 6t
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23 Feb 2021, 07:38
23 Feb 2021, 07:38
1
Carcass wrote:
If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?
A. 20
B. 30
C. 50
D. 60
E. 90
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 20
B. 30
C. 50
D. 60
E. 90
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Given: \(x + y = 6t\)
Square both sides to get: \((x + y)^2 = (6t)^2\)
Expand and simplify: \(x^2 + 2xy + y^2 = 36t^2\)
Also given: \(xy = -7t^2\)
Multiply both sides by 2 to get: \(2xy = -14t^2\)
We now have two equations:
\(x^2 + 2xy + y^2 = 36t^2\)
\(2xy = -14t^2\)
Subtract the bottom equation from the top equation to get: \(x^2 + y^2 = 50t^2\)
Our goal is to find the value of \(\frac{(x^2 + y^2)}{t^2}\)
Replace the numerator with its equivalent value to get: \(\frac{50t^2}{t^2}\)
Simplify to get: 50
Answer: C
Cheers,
Brent
