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If x + y/x − y
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26 Feb 2021, 06:44
26 Feb 2021, 06:44
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Question Stats:
93% (01:23) correct
6% (02:27) wrong based on 31 sessions
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If \(\frac{x + y}{x − y} = \frac{1}{2}\), then \(\frac{xy + x^2}{xy − x^2}=\)
(A) –4.2
(B) –1/2
(C) 1.1
(D) 3
(E) 5.3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) –4.2
(B) –1/2
(C) 1.1
(D) 3
(E) 5.3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: If x + y/x − y
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26 Feb 2021, 07:04
26 Feb 2021, 07:04
Carcass wrote:
If \(\frac{x + y}{x − y} = \frac{1}{2}\), then \(\frac{xy + x^2}{xy − x^2}=\)
(A) –4.2
(B) –1/2
(C) 1.1
(D) 3
(E) 5.3
(A) –4.2
(B) –1/2
(C) 1.1
(D) 3
(E) 5.3
Given: \(\frac{xy + x^2}{xy − x^2}\)
Factor numerator and denominator to get: \(\frac{x(y + x)}{x(y − x)}\)
Rewrite as follows: \((\frac{x}{x})(\frac{(y + x)}{(y − x)})\)
Simplify to get: \(\frac{(x + y)}{(y − x)}\)
Notice that this fraction ALMOST matches the given information \(\frac{x + y}{x − y} = \frac{1}{2}\).
No problem...
\(\frac{(x + y)}{(y − x)}=\frac{(x + y)}{-1(-y + x)}=\frac{(x + y)}{-1(x - y)}=(\frac{1}{-1})(\frac{(x + y)}{(x - y)})=(-1)(\frac{1}{2})=-\frac{1}{2}\)
Answer: B
If x + y/x − y
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26 Feb 2021, 07:11
26 Feb 2021, 07:11
1
Solution:
\(\frac{x+y}{x-y}=\frac{1}{2}\)
Cross multiply to get,
2(x+y)=x-y
2x+2y=x-y
2x-x=-2y-y
x(2-1)=-y(2+1)
x=-3y
Thus, when x=-3, y=1
Substitute the above value to get the answer
\(\frac{-3+9}{-3-9}=\frac{6}{-12}=\frac{-1}{2}\)
IMO B
Hope this helps!
\(\frac{x+y}{x-y}=\frac{1}{2}\)
Cross multiply to get,
2(x+y)=x-y
2x+2y=x-y
2x-x=-2y-y
x(2-1)=-y(2+1)
x=-3y
Thus, when x=-3, y=1
Substitute the above value to get the answer
\(\frac{-3+9}{-3-9}=\frac{6}{-12}=\frac{-1}{2}\)
IMO B
Hope this helps!
