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If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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19 Dec 2010, 17:04
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If 6xy = \(x^2\)y + 9y, what is the value of xy? (1) x = –2 (2) x < 0 The answer is D, with the following explanation: The equation in question can be rephrased as follows:
x2y – 6xy + 9y = 0 y(x2 – 6x + 9) = 0 y(x – 3)2 = 0
Therefore, one or both of the following must be true: y = 0 or x = 3
It follows that the product xy must equal either 0 or 3y. This question can therefore be rephrased several different ways: "What is y?" or "Does x = 3?"
(1) SUFFICIENT: If x = 2, then: (–2)2y – 6(–2)y + 9y = 0 4y + 12y + 9y = 0 25y = 0
Therefore y = xy = 0. Tn fact, for any value of x other than 3, y must equal zero.
(2) SUFFICIENT: x is negative. Therefore, x cannot equal 3, and it follows that y = 0. Therefore, xy = 0.
The correct answer is D.
What I did, i simply applied the info from statement 1, and got that 12Y=13Y which can only be true if Y is 0 and therefore, XY is 0. In the second statement, i did the same and the result came to be the same. Is this faulty reasoning? Also, this is said to be 700800 level question and my way seems just too easy to solve such a high level problem...
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Re: If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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MisterEko wrote: Guys, I just have a question if my way of solving it is reasonable and can often be applied here. I got the right answer on this one, but am not sure it would work usually: If 6xy = x2y + 9y, what is the value of xy? (1) x = –2 (2) x < 0 The answer is D, with the following explanation: The equation in question can be rephrased as follows:
x2y – 6xy + 9y = 0 y(x2 – 6x + 9) = 0 y(x – 3)2 = 0
Therefore, one or both of the following must be true: y = 0 or x = 3
It follows that the product xy must equal either 0 or 3y. This question can therefore be rephrased several different ways: "What is y?" or "Does x = 3?"
(1) SUFFICIENT: If x = 2, then: (–2)2y – 6(–2)y + 9y = 0 4y + 12y + 9y = 0 25y = 0
Therefore y = xy = 0. Tn fact, for any value of x other than 3, y must equal zero.
(2) SUFFICIENT: x is negative. Therefore, x cannot equal 3, and it follows that y = 0. Therefore, xy = 0.
The correct answer is D. What I did, i simply applied the info from statement 1, and got that 12Y=13Y which can only be true if Y is 0 and therefore, XY is 0. In the second statement, i did the same and the result came to be the same. Is this faulty reasoning? Also, this is said to be 700800 level question and my way seems just too easy to solve such a high level problem... For statement (1) your reasoning looks OK. As for statement (2) what do you mean by "did the same"? One can also do this way: \(6xy=x^2y + 9y\) > \(y(x^26x+9)=0\) > \(y(x3)^2=0\) > either \(x=3\) or \(y=0\) (or both). (1) x = –2 > so \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. (2) x < 0 > again \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. Answer: D. Check question #1 here: inequalityandabsolutevaluequestionsfrommycollection86939.html for harder version of the same problem. Hope it helps.
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Re: If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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19 Dec 2010, 18:01
Bunuel wrote: MisterEko wrote: Guys, I just have a question if my way of solving it is reasonable and can often be applied here. I got the right answer on this one, but am not sure it would work usually: If 6xy = x2y + 9y, what is the value of xy? (1) x = –2 (2) x < 0 The answer is D, with the following explanation: The equation in question can be rephrased as follows:
x2y – 6xy + 9y = 0 y(x2 – 6x + 9) = 0 y(x – 3)2 = 0
Therefore, one or both of the following must be true: y = 0 or x = 3
It follows that the product xy must equal either 0 or 3y. This question can therefore be rephrased several different ways: "What is y?" or "Does x = 3?"
(1) SUFFICIENT: If x = 2, then: (–2)2y – 6(–2)y + 9y = 0 4y + 12y + 9y = 0 25y = 0
Therefore y = xy = 0. Tn fact, for any value of x other than 3, y must equal zero.
(2) SUFFICIENT: x is negative. Therefore, x cannot equal 3, and it follows that y = 0. Therefore, xy = 0.
The correct answer is D. What I did, i simply applied the info from statement 1, and got that 12Y=13Y which can only be true if Y is 0 and therefore, XY is 0. In the second statement, i did the same and the result came to be the same. Is this faulty reasoning? Also, this is said to be 700800 level question and my way seems just too easy to solve such a high level problem... For statement (1) your reasoning looks OK. As for statement (2) what do you mean by "did the same"? One can also do this way: \(6xy=x^2y + 9y\) > \(y(x^26x+9)=0\) > \(y(x3)^2=0\) > either \(x=3\) or \(y=0\) (or both). (1) x = –2 > so \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. (2) x < 0 > again \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. Answer: D. Check question #1 here: inequalityandabsolutevaluequestionsfrommycollection86939.html for harder version of the same problem. Hope it helps. Thanks a lot. What I meant by "I did the same" is that I substituted x for 1 and tested, and result came out to be the same...
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Re: If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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Re: If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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11 Dec 2013, 04:14
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Bunuel wrote: MisterEko wrote: Guys, I just have a question if my way of solving it is reasonable and can often be applied here. I got the right answer on this one, but am not sure it would work usually: If 6xy = x2y + 9y, what is the value of xy? (1) x = –2 (2) x < 0 The answer is D, with the following explanation: The equation in question can be rephrased as follows:
x2y – 6xy + 9y = 0 y(x2 – 6x + 9) = 0 y(x – 3)2 = 0 Therefore, one or both of the following must be true: y = 0 or x = 3
It follows that the product xy must equal either 0 or 3y. This question can therefore be rephrased several different ways: "What is y?" or "Does x = 3?"
(1) SUFFICIENT: If x = 2, then: (–2)2y – 6(–2)y + 9y = 0 4y + 12y + 9y = 0 25y = 0
Therefore y = xy = 0. Tn fact, for any value of x other than 3, y must equal zero.
(2) SUFFICIENT: x is negative. Therefore, x cannot equal 3, and it follows that y = 0. Therefore, xy = 0.
The correct answer is D. What I did, i simply applied the info from statement 1, and got that 12Y=13Y which can only be true if Y is 0 and therefore, XY is 0. In the second statement, i did the same and the result came to be the same. Is this faulty reasoning? Also, this is said to be 700800 level question and my way seems just too easy to solve such a high level problem... For statement (1) your reasoning looks OK. As for statement (2) what do you mean by "did the same"? One can also do this way: \(6xy=x^2y + 9y\) > \(y(x^26x+9)=0\) > \(y(x3)^2=0\) > either \(x=3\) or \(y=0\) (or both). (1) x = –2 > so \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. (2) x < 0 > again \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. Answer: D. Check question #1 here: inequalityandabsolutevaluequestionsfrommycollection86939.html for harder version of the same problem. Hope it helps. Hi Bunuel, I am still not clear why do we need statements. Once we know that y=0 then no matter what the value of x is xy will always be =0. Do we need to even consider the statements. Am I thinking in the right direction or is there a disconnect somewhere.



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Re: If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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11 Dec 2013, 04:31
davidfrank wrote: Bunuel wrote: MisterEko wrote: Guys, I just have a question if my way of solving it is reasonable and can often be applied here. I got the right answer on this one, but am not sure it would work usually: If 6xy = x2y + 9y, what is the value of xy? (1) x = –2 (2) x < 0 The answer is D, with the following explanation: The equation in question can be rephrased as follows:
x2y – 6xy + 9y = 0 y(x2 – 6x + 9) = 0 y(x – 3)2 = 0 Therefore, one or both of the following must be true: y = 0 or x = 3
It follows that the product xy must equal either 0 or 3y. This question can therefore be rephrased several different ways: "What is y?" or "Does x = 3?"
(1) SUFFICIENT: If x = 2, then: (–2)2y – 6(–2)y + 9y = 0 4y + 12y + 9y = 0 25y = 0
Therefore y = xy = 0. Tn fact, for any value of x other than 3, y must equal zero.
(2) SUFFICIENT: x is negative. Therefore, x cannot equal 3, and it follows that y = 0. Therefore, xy = 0.
The correct answer is D. What I did, i simply applied the info from statement 1, and got that 12Y=13Y which can only be true if Y is 0 and therefore, XY is 0. In the second statement, i did the same and the result came to be the same. Is this faulty reasoning? Also, this is said to be 700800 level question and my way seems just too easy to solve such a high level problem... For statement (1) your reasoning looks OK. As for statement (2) what do you mean by "did the same"? One can also do this way: \(6xy=x^2y + 9y\) > \(y(x^26x+9)=0\) > \(y(x3)^2=0\) > either \(x=3\) or \(y=0\) (or both). (1) x = –2 > so \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. (2) x < 0 > again \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. Answer: D. Check question #1 here: inequalityandabsolutevaluequestionsfrommycollection86939.html for harder version of the same problem. Hope it helps. Hi Bunuel, I am still not clear why do we need statements. Once we know that y=0 then no matter what the value of x is xy will always be =0. Do we need to even consider the statements. Am I thinking in the right direction or is there a disconnect somewhere. See the red part is not true. We don't know whether \(y=0\). From \(y(x3)^2=0\) we have that \(x=3\) OR \(y=0\). Now, if \(x=3\), then y can be any number, thus xy is not necessarily 0. Hope it's clear.
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Re: If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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11 Dec 2013, 06:21
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MisterEko wrote: If 6xy = x^2y + 9y, what is the value of xy?
(1) x = –2 (2) x < 0
Responding to a pm: Why do we need the statements? Given: \(6xy = x^2y + 9y\) Given: \(y(x3)^2 = 0\) What we know is this: EITHER y is 0 OR x is 3. It is possible that both y is 0 and x is 3 but at least one of them MUST be true. This is all we know. We don't know whether y is 0 or whether x is 3 or both. Question: what is xy? I cannot say yet. All I know is that either y is 0 or x is 3. If y is 0, xy will be 0. If x is 3, then I don't know y which could be anything so xy could be anything. So I cannot say what xy is. (1) x = –2 This tells me that x is not 3. If x is not 3, y MUST be 0 because one of them has to be true. If y is 0, we know for sure that xy is 0. Sufficient. (2) x < 0 This again tells me that x is not 3. If x is not 3, y MUST be 0 because one of them has to be true. If y is 0, we know for sure that xy is 0. Sufficient. Answer (D)
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Re: If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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17 Sep 2015, 08:53
Bunuel wrote: MisterEko wrote: Guys, I just have a question if my way of solving it is reasonable and can often be applied here. I got the right answer on this one, but am not sure it would work usually: If 6xy = x2y + 9y, what is the value of xy? (1) x = –2 (2) x < 0 The answer is D, with the following explanation: The equation in question can be rephrased as follows:
x2y – 6xy + 9y = 0 y(x2 – 6x + 9) = 0 y(x – 3)2 = 0
Therefore, one or both of the following must be true: y = 0 or x = 3
It follows that the product xy must equal either 0 or 3y. This question can therefore be rephrased several different ways: "What is y?" or "Does x = 3?"
(1) SUFFICIENT: If x = 2, then: (–2)2y – 6(–2)y + 9y = 0 4y + 12y + 9y = 0 25y = 0
Therefore y = xy = 0. Tn fact, for any value of x other than 3, y must equal zero.
(2) SUFFICIENT: x is negative. Therefore, x cannot equal 3, and it follows that y = 0. Therefore, xy = 0.
The correct answer is D. What I did, i simply applied the info from statement 1, and got that 12Y=13Y which can only be true if Y is 0 and therefore, XY is 0. In the second statement, i did the same and the result came to be the same. Is this faulty reasoning? Also, this is said to be 700800 level question and my way seems just too easy to solve such a high level problem... For statement (1) your reasoning looks OK. As for statement (2) what do you mean by "did the same"? One can also do this way: \(6xy=x^2y + 9y\) > \(y(x^26x+9)=0\) > \(y(x3)^2=0\) > either \(x=3\) or \(y=0\) (or both). (1) x = –2 > so \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. (2) x < 0 > again \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient. Answer: D. Check question #1 here: inequalityandabsolutevaluequestionsfrommycollection86939.html for harder version of the same problem. Hope it helps. why we can not cancel out Y from 6xy=x^2y + 9y ? this is not inequality..what is mistake in my thinking



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Re: If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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17 Sep 2015, 20:24
anupamadw wrote: why we can not cancel out Y from 6xy=x^2y + 9y ? this is not inequality..what is mistake in my thinking
Usually, it is not a good idea to cancel out a variable. You lose a solution if you do. If you do not cancel out the y, you get that this inequality: 6xy=x^2y + 9y holds when either x = 3 or y = 0. If you do cancel out the y, you get that this inequality: 6xy=x^2y + 9y holds when x = 3. You lost the y = 0 value. Hence, it's always better to take out y common and keep it on the side, not cancel it.
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If 6xy = x^2y + 9y, what is the value of xy? [#permalink]
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31 Dec 2017, 06:42
[quote="MisterEko"]If 6xy = \(x^2\)y + 9y, what is the value of xy?
(1) x = –2 (2) x < 0
[spoiler=]The answer is D, with the following explanation: The equation in question can be rephrased as follows:
Slightly different analysis. Bunuel / Experts pl. validate
Given \(6xy=x^2y+9y\)
Find xy= ?
Now \(6xy=x^2y+9y\)  (1) => \(6xy=y(x^2+9)\) => \(6x=x^2+9\) => \(x^26x+9=0\) => \(x^23x3x+9=0\) => \((x3)^2=0\) => Therefore x=3 => Substituting x=3 in (1) we have => 0=0
So we know the value of 'x'. We need to find y=?
Statement 1 x=2 => Substituting in (1) we have => 12y=13y => OR 25y=0 => OR y=0 => Therefore xy=0 SUFFICIENT
Statement 2 x<0 i.e 'x' is ve => Substituting value of 'x' in equ (1) => Now irrespective of the magnitude ' x ' LHS of equ (1) will be ve => i.e 6xy= ky  for some constant 'k' => Again irrespective of the magnitude ' x ' RHS of equ (1) will be +ve => i.e \(x^2y+9y=my\)  for some constant 'm' => ky=my => OR my+ky=0 => OR ny=0  for some constant 'n' => Irrespective of the SIGN of n, y=0 => Therefore xy=0. SUFFICIENT
Therefore "D"
Thanks Dinesh




If 6xy = x^2y + 9y, what is the value of xy?
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