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If (3x + 2y - 22)^2 + (4x - 5y + 9)^2 = 0 and 5x - 4y = 0, then what
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03 Mar 2021, 02:25
03 Mar 2021, 02:25
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If \((3x + 2y - 22)^2 + (4x - 5y + 9)^2 = 0\) and \(5x - 4y = 0\), then what is the value of x + y ?
A. 7
B. 8
C. 9
D. 11
E. 13
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 7
B. 8
C. 9
D. 11
E. 13
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 (3x + 2y - 22)^2 + (4x - 5y + 9)^2 = 0 and 5x - 4y = 0, then what
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03 Mar 2021, 07:31
03 Mar 2021, 07:31
8
Carcass wrote:
If \((3x + 2y - 22)^2 + (4x - 5y + 9)^2 = 0\) and \(5x - 4y = 0\), then what is the value of x + y ?
A. 7
B. 8
C. 9
D. 11
E. 13
A. 7
B. 8
C. 9
D. 11
E. 13
Key concept: k² ≥ 0, for all values of k.
So, if something² + (something else)² = 0, then we can be certain that: something = 0 and (something else) = 0
Likewise, since (3x + 2y - 22)² + (4x - 5y + 9)² = 0 , we know that 3x + 2y - 22 = 0 and 4x - 5y + 9 = 0
I'm going to ignore the first equation, 3x + 2y - 22 = 0
Instead, notice that, if we take the other equation, 4x - 5y + 9 = 0 and combine it with the given equation, 5x - 4y = 0, we can quickly find the value of x + y without having to solve for the individual values of x and y.
We have:
5x - 4y = 0
4x - 5y + 9 = 0
Rewrite the bottom equation as follows:
5x - 4y = 0
4x - 5y = -9
Subtract the bottom equation from the top equation to get: x + y = 9
Answer: C
Cheers,
Brent
General Discussion
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
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Re: If (3x + 2y - 22)^2 + (4x - 5y + 9)^2 = 0 and 5x - 4y = 0, then what
[#permalink]
03 Mar 2021, 04:22
03 Mar 2021, 04:22
3
Carcass wrote:
If \((3x + 2y - 22)^2 + (4x - 5y + 9)^2 = 0\) and \(5x - 4y = 0\), then what is the value of x + y ?
A. 7
B. 8
C. 9
D. 11
E. 13
A. 7
B. 8
C. 9
D. 11
E. 13
Excellent Question Carcass
Guys, don't fall for \((a + b + c)^2\) formula, you will be just wasting your 4-5 minutes!
We are given that \((3x + 2y - 22)^2 + (4x - 5y + 9)^2 = 0\) and \(5x - 4y = 0\)
Let,
\((3x + 2y - 22) = a\)
\((4x - 5y + 9) = b\)
i.e. \(a^2 + b^2 = 0\)
The given condition is true when both a and b are zero
3x + 2y - 22 = 0
3x + 2y = 22 ...... (1)
4x - 5y + 9 = 0
4x - 5y = -9 ...... (2)
Multiply (1) by 4 and (2) by 3;
12x + 8y = 88
12x - 15y = -27
Solve these 2 simultaneous equations to get x = 4 and y = 5
So, x + y = 9
Hence, option C
