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16 Sep 2014, 01:24
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Given that \(5x=125-3y+z\) and \(\sqrt{5x}-5-\sqrt{z-3y}=0\), what is the value of \(\sqrt{\frac{45(z-3y)}{x} }\)?
A. 5
B. 10
C. 15
D. 20
E. cannot be determined
A. 5
B. 10
C. 15
D. 20
E. cannot be determined
16 Sep 2014, 01:24
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Official Solution:
Given that \(5x=125-3y+z\) and \(\sqrt{5x}-5-\sqrt{z-3y}=0\), what is the value of \(\sqrt{\frac{45(z-3y)}{x} }\)?
A. 5
B. 10
C. 15
D. 20
E. cannot be determined
By rearranging both expressions, we get: \(5x-(z-3y)=125\) and \(\sqrt{5x}-\sqrt{z-3y}=5\). Let's denote \(\sqrt{5x}\) as \(a\) and \(\sqrt{z-3y}\) as \(b\).
So we have \(a^2-b^2=125\) and \(a-b=5\). Now, \(a^2-b^2=(a-b)(a+b)=125\) and as \(a-b=5\), then \((a-b)(a+b)=5*(a+b)=125\), which implies that \(a+b=25\).
This gives us two equations with two unknowns: \(a+b=25\) and \(a-b=5\). Solving for \(a\) yields \(a=15=\sqrt{5x}\), so \(x=45\). Solving for \(b\) yields \(b=10=\sqrt{z-3y}\).
Finally, \(\sqrt{\frac{45(z-3y)}{x} }=\sqrt{\frac{45*10^2}{45} }=10\).
Answer: B
Given that \(5x=125-3y+z\) and \(\sqrt{5x}-5-\sqrt{z-3y}=0\), what is the value of \(\sqrt{\frac{45(z-3y)}{x} }\)?
A. 5
B. 10
C. 15
D. 20
E. cannot be determined
By rearranging both expressions, we get: \(5x-(z-3y)=125\) and \(\sqrt{5x}-\sqrt{z-3y}=5\). Let's denote \(\sqrt{5x}\) as \(a\) and \(\sqrt{z-3y}\) as \(b\).
So we have \(a^2-b^2=125\) and \(a-b=5\). Now, \(a^2-b^2=(a-b)(a+b)=125\) and as \(a-b=5\), then \((a-b)(a+b)=5*(a+b)=125\), which implies that \(a+b=25\).
This gives us two equations with two unknowns: \(a+b=25\) and \(a-b=5\). Solving for \(a\) yields \(a=15=\sqrt{5x}\), so \(x=45\). Solving for \(b\) yields \(b=10=\sqrt{z-3y}\).
Finally, \(\sqrt{\frac{45(z-3y)}{x} }=\sqrt{\frac{45*10^2}{45} }=10\).
Answer: B
General Discussion
MbaRacer
Joined: 17 Sep 2014
Last visit: 28 Jan 2020
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Location: India
Concentration: Operations, Strategy
Schools: Broad '20 (M$) Owen '20 (A) WP Carey" 20 (D) Jones '20 (WL) Rutgers '20 (A) Goizueta '20 (WL) Krannert '20 (A)
GMAT 1: 710 Q49 V38
GPA: 3.65
WE:Engineering (Manufacturing)
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Schools: Broad '20 (M$) Owen '20 (A) WP Carey" 20 (D) Jones '20 (WL) Rutgers '20 (A) Goizueta '20 (WL) Krannert '20 (A)
GMAT 1: 710 Q49 V38
Posts: 139
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11 Oct 2016, 23:24
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Bunuel
Will sqrt(10^2) not yield +/- 10 ?
