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13 Oct 2016, 08:40
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
73% (02:57) correct
27%
(03:06)
wrong
based on 535
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If y = x - 3, and x^2 - 5y^2 + 4xy - 15 = 0, then x + 2y =
A. 2
B. 4
C. 6
D. 8
E. 10
A. 2
B. 4
C. 6
D. 8
E. 10
I can think of 3 different solutions to this question.
Kudos for all correct solutions
A video solution can be found here: https://www.gmatprepnow.com/module/gmat ... video/1020
Kudos for all correct solutions
A video solution can be found here: https://www.gmatprepnow.com/module/gmat ... video/1020
Solving this question helps.
Taking a timed set of similar questions in
GMAT Club Forum Quiz →
is even better.
14 Oct 2016, 07:36
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GMATPrepNow
Another approach:
We're also told that y = x - 3
Rearrange to get: x - y = 3
Also given: x² - 5y² + 4xy - 15 = 0
Add 15 to both sides: x² - 5y² + 4xy = 15
Rearrange to get: x² + 4xy - 5y² = 15
Factor: (x - y)(x + 5y) = 15
Replace x - y with 3 to get: 3(x + 5y) = 15
So, we can conclude that (x + 5y) = 5
We have two equations:
x + 5y = 5
x - y = 3
ADD the two above equations to get: 2x + 4y = 8
Divide both sides by 2 to get: x + 2y = 4
Answer: Here's the video solution: https://www.gmatprepnow.com/module/gmat ... video/1020
Cheers,
Brent
13 Oct 2016, 21:14
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From given information, \(y = x-3\) we can get \((x-y)^2 = 9\)
Rewriting the other equation, we get
\((x-y)^2 + 6xy - 6y^ 2= 15 \) -> \(9 = 15 + 6y(y-x)\) -> \(-6 = -18 y\) (as \(y-x = -3\))
\(y = \frac{1}{3}\) and solving for x, x = \(\frac{10}{3}\)
Therefore, the value of x+2y is \(\frac{12}{3}\)(Option B)
Rewriting the other equation, we get
\((x-y)^2 + 6xy - 6y^ 2= 15 \) -> \(9 = 15 + 6y(y-x)\) -> \(-6 = -18 y\) (as \(y-x = -3\))
\(y = \frac{1}{3}\) and solving for x, x = \(\frac{10}{3}\)
Therefore, the value of x+2y is \(\frac{12}{3}\)(Option B)
