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what is the value of xy

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Oct 12, 2016 4:09 am
If 6xy = x²y + 9y, what is the value of xy?

(1) x = -2

(2) x < 0
Target question: What is the value of xy?

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

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by Needgmat » Wed Oct 12, 2016 6:24 am
Brent@GMATPrepNow wrote:
If 6xy = x²y + 9y, what is the value of xy?

(1) x = -2

(2) x < 0
Target question: What is the value of xy?

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.

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by richachampion » Wed Oct 12, 2016 8:56 am
Brent@GMATPrepNow wrote: Answer = D

RELATED VIDEO
- Solving quadratic equations: https://www.gmatprepnow.com/module/gmat ... /video/964

Cheers,
Brent
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by Scott@TargetTestPrep » Sun Oct 16, 2016 5:24 pm
If 6xy = x²y + 9y, what is the value of xy?

(1) x = -2

(2) x < 0
We are given that 6xy = (x^2)y + 9y and need to determine the value of xy.

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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by fiza gupta » Mon Oct 17, 2016 2:15 am
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
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