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If y = x  3, and x²  5y²
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13 Oct 2016, 08:40
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77% (02:40) correct 23% (03:06) wrong based on 107 sessions
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If y = x  3, and x²  5y² + 4xy  15 = 0, then x + 2y = 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
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Re: If y = x  3, and x²  5y²
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13 Oct 2016, 10:03
Substitute the value of y in the given equation:
x^2  5(x  3)^2 + 4x(x  3)  15 = 0 x^2  (x  3)(5x  15  4x)  15 = 0 x^2  (x  3)(x  15)  15 = 0 x^2  x^2 + 18x  45  15 = 0 x = 10/3 > y = 1/3
x + 2y = 10/3 + 2(1/3) = 12/3 = 4
Answer: B



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Re: If y = x  3, and x²  5y²
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13 Oct 2016, 10:54
(yx)^2=9 Substitute this in the other equation, Final : y= 1/3 x=10/3. Hence, 4 Sent from my Nexus 5X using GMAT Club Forum mobile app



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Re: If y = x  3, and x²  5y²
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13 Oct 2016, 21:14
From given information, y = x3 we can get (xy)^2 = 9 Rewriting the other eqn, we get (xy)^2 + 6xy  6y^ 2= 15 9 = 15 + 6y(yx) 6 = 18 y (because yx = 3) y = 1/3. We can get x = 10/3 x+2y = 12/3(Option B)
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Re: If y = x  3, and x²  5y²
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14 Oct 2016, 07:16
Hi Brent,
I have solved the question like above mentioned solutions. However, I'm curious to see if you have another short cut or though to solve it.
Thaknks



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Re: If y = x  3, and x²  5y²
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14 Oct 2016, 07:36
GMATPrepNow wrote: If y = x  3, and x²  5y² + 4xy  15 = 0, then x + 2y =
A) 2 B) 4 C) 6 D) 8 E) 10
Another approach: We're also told that y = x  3 Rearrange to get: x  y = 3Also 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/1020Cheers, Brent
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Re: If y = x  3, and x²  5y²
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24 Oct 2016, 19:39
y=x3 x^2  5y^2 +4xy 15 =0
x^25(x^2 6x+9)+4x(x3)15=0 6(3x10) = 0 x = 10/3
x+2(x3) = 10/3 + 20/3  6 = 4



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Re: If y = x  3, and x²  5y²
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08 Mar 2019, 16:26
GMATPrepNow wrote: GMATPrepNow wrote: If y = x  3, and x²  5y² + 4xy  15 = 0, then x + 2y =
A) 2 B) 4 C) 6 D) 8 E) 10
Another approach: We're also told that y = x  3 Rearrange to get: x  y = 3Also 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/1020Cheers, Brent Hello GMATPrepNow ! Would you please give a detailed explanation about how did you factorize? Rearrange to get: x² + 4xy  5y² = 15 Factor: (x  y)(x + 5y) = 15 Thank you so much!



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Re: If y = x  3, and x²  5y²
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09 Mar 2019, 08:10
jfranciscocuencag wrote: Hello GMATPrepNow ! Would you please give a detailed explanation about how did you factorize? Rearrange to get: x² + 4xy  5y² = 15 Factor: (x  y)(x + 5y) = 15 Thank you so much! You bet! First, IGNORE the y's in the expression to get: x² + 4x  5 = 15 We can now factor the left side to get: (x + 5)(x  1) = 15 At this point, we need to add some y's. Notice that the last term = 5y² To get 5y², we need to add a y to each binomial to get: (x + 5 y)(x  1 y) = 15 Does that help? Cheers, Brent
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Re: If y = x  3, and x²  5y²
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