If 6xy = x2y + 9y, what is the value of xy?
(1) x = -2
(2) x < 0
OAD
what is the value of xy
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Target question: What is the value of xy?If 6xy = x²y + 9y, what is the value of xy?
(1) x = -2
(2) x < 0
Given: 6xy = x²y + 9y
Set equal to zero: x²y - 6xy + 9y = 0
Factor: y(x² - 6x + 9) = 0
Factor more: y(x - 3)(x - 3) = 0
For the above equation to hold true, it must be the case that y = 0 or x = 3
Statement 1: x = -2
This tells us that x does NOT equal 3.
If x does NOT equal 3, then y must equal 0 (see above in bold)
If y = 0, then xy must equal 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x < 0
This is yet another way to tell us that x does not equal 3.
If x does not equal 3, then y must equal 0 (see above in bold)
If y = 0, then xy must equal 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
RELATED VIDEO
- Solving quadratic equations: https://www.gmatprepnow.com/module/gmat ... /video/964
Cheers,
Brent
Brent@GMATPrepNow wrote:Target question: What is the value of xy?If 6xy = x²y + 9y, what is the value of xy?
(1) x = -2
(2) x < 0
Given: 6xy = x²y + 9y
Set equal to zero: x²y - 6xy + 9y = 0
Factor: y(x² - 6x + 9) = 0
Factor more: y(x - 3)(x - 3) = 0
For the above equation to hold true, it must be the case that y = 0 or x = 3
Statement 1: x = -2
This tells us that x does NOT equal 3.
If x does NOT equal 3, then y must equal 0 (see above in bold)
If y = 0, then xy must equal 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x < 0
This is yet another way to tell us that x does not equal 3.
If x does not equal 3, then y must equal 0 (see above in bold)
If y = 0, then xy must equal 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
RELATED VIDEO
- Solving quadratic equations: https://www.gmatprepnow.com/module/gmat ... /video/964
Cheers,
Brent
Hi Brent ,
Thank you so much for your explanation. It really helps.
Thanks,
Kavin
- richachampion
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Fantastic Solution Sir.Brent@GMATPrepNow wrote: Answer = D
RELATED VIDEO
- Solving quadratic equations: https://www.gmatprepnow.com/module/gmat ... /video/964
Cheers,
Brent
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We are given that 6xy = (x^2)y + 9y and need to determine the value of xy.If 6xy = x²y + 9y, what is the value of xy?
(1) x = -2
(2) x < 0
We can start by manipulating the given equation and factoring out y.
6xy = (x^2)y + 9y
(x^2)y - 6xy + 9y = 0
y(x^2 - 6x + 9) = 0
y(x - 3)(x - 3) = 0
y = 0 or x = 3
Statement One Alone:
x = -2
Since x = -2, the only way for y(x - 3)(x - 3) to equal zero is if y = 0 and thus xy = 0. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
x < 0
Since x < 0, the only way for y(x - 3)(x - 3) to equal zero is if y = 0 and thus xy = 0. Statement two alone is sufficient.
Answer: D
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- fiza gupta
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Given: 6xy = x2y + 9y
y(x^2+9-6x) = 0
y(x-3)^2 = 0
either y = 0 or x = 3 or both will be true
1) x = -2
x is not equal to 3
so Y = 0
xy = 0
SUFFICIENT
2) x < 0
x is not equal to 3
so Y = 0
xy = 0
SUFFICIENT
SO D
y(x^2+9-6x) = 0
y(x-3)^2 = 0
either y = 0 or x = 3 or both will be true
1) x = -2
x is not equal to 3
so Y = 0
xy = 0
SUFFICIENT
2) x < 0
x is not equal to 3
so Y = 0
xy = 0
SUFFICIENT
SO D
Fiza Gupta