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If 1/y − 1/(y+1) = 1/(y+4), what is the sum of all solutions for y?
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28 Feb 2021, 10:29
28 Feb 2021, 10:29
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If \(\frac{1}{y} − \frac{1}{(y+1)} = \frac{1}{(y+4)}\), what is the sum of all solutions for y?
A. -2
B. -1
C. 0
D. 1
E. 2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -2
B. -1
C. 0
D. 1
E. 2
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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WE:Education (Education)
Re: If 1/y − 1/(y+1) = 1/(y+4), what is the sum of all solutions for y?
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28 Feb 2021, 12:08
28 Feb 2021, 12:08
1
Carcass wrote:
If \(\frac{1}{y} − \frac{1}{(y+1)} = \frac{1}{(y+4)}\), what is the sum of all solutions for y?
A. -2
B. -1
C. 0
D. 1
E. 2
A. -2
B. -1
C. 0
D. 1
E. 2
\(\frac{1}{y} − \frac{1}{(y+1)} = \frac{1}{(y+4)}\)
\(\frac{{(y+1) - y}}{y(y+1)} = \frac{1}{(y+4)}\)
\(\frac{1}{y(y+1)} = \frac{1}{(y+4)}\)
\(y + 4= y(y+1)\)
\(y + 4 = y^2 + y\)
\(4 = y^2 \)
i.e. \(y = ±2\)
Sum of \(+2\) and \(-2\) is \(0\)
Hence, option C
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 1/y − 1/(y+1) = 1/(y+4), what is the sum of all solutions for y?
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28 Feb 2021, 15:33
28 Feb 2021, 15:33
1
Carcass wrote:
If \(\frac{1}{y} − \frac{1}{(y+1)} = \frac{1}{(y+4)}\), what is the sum of all solutions for y?
A. -2
B. -1
C. 0
D. 1
E. 2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -2
B. -1
C. 0
D. 1
E. 2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Given: \(\frac{1}{y} − \frac{1}{(y+1)} = \frac{1}{(y+4)}\)
To eliminate the fractions, we'll multiply both sides of the equation by the least common multiple of y, y+1, and y+4
So, multiply both sides by (y)(y+1)(y+4) to get: (y+1)(y+4) - (y)(y+4) = (y)(y+1)
Expand to get: [y² + 5y + 4] - [y² + 4y] = y² + y
Simplify: y + 4 = y² + y
Subtract y from both sides to get: 4 = y²
So, y = 2 or y = -2
The SUM of the solutions = 2 + (-2) = 0
Answer: C
Cheers,
Brent
