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If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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20 Apr 2010, 07:27
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If x^3*y = 24, what is the value of x^3*y^3  x^2*y^2? (1) x^2*y^2 = 36. (2) x^3*y^2 = 72.
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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20 Apr 2010, 08:13
Hussain15 wrote: If \(X^3Y = 24\), what is the value of \(X^3Y^3\) – \(X^2Y^2\)? (1) \(X^2Y^2 = 36\). (2) \(X^3Y^2 = 72\). 1. you can write it as X*X*Y*Y = 36. there are 2 pairs of X*Y so X*Y = +6 since we dont know if the 6 is positive or negative and the questions has you raise to an odd power A is INSUFF 2. we know from the question X^3 * Y =24 and this choice has an extra Y so the difference is a factor of 3 so Y=3. now plugging back in Y you find X=2 so SUFF. B
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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20 Apr 2010, 08:40
IMO D Both the equations are seems to be solvable but only catch is to check the condition of ve and +ve we need to find the value of \(x^3y^3x^2y^2 = x^3 *y *y^2  x^2y^2\) = \(y^2(24x^2)\) since it involved square values of both x and y , thus ve value of y will not have any effect. Thus D
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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20 Apr 2010, 09:04
gurpreetsingh wrote: IMO D
Both the equations are seems to be solvable but only catch is to check the condition of ve and +ve
we need to find the value of \(x^3y^3x^2y^2 = x^3 *y *y^2  x^2y^2\)
= \(y^2(24x^2)\)
since it involved square values of both x and y , thus ve value of y will not have any effect.
Thus D hmm. well if you expand that out you can get: 24*y^2  36. How do you proceed from here to find a numerical answer?
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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20 Apr 2010, 09:33
solve the equation x^3 * y = 24 with both the individual statements. It will always give you solution as 2 equations are there. Now the only catch was of ve and +ve values of x and y. which i have proved above wont affect the answer. Just try to solve the given equation with the equations given in statement separately.
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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25 Sep 2010, 02:31
gurpreetsingh wrote: solve the equation x^3 * y = 24 with both the individual statements. It will always give you solution as 2 equations are there. Now the only catch was of ve and +ve values of x and y. which i have proved above wont affect the answer. Just try to solve the given equation with the equations given in statement separately. your posts continue to prove that I need to work hard...harder hardest ...cheers +1



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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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25 Sep 2010, 03:08
\(X^3*Y = 24\) => Either x and y are both negative or both positive. \(X^3*Y^3  X^2*Y^2\) = \(X^2*Y^2 *(X*Y 1)\) Statement 1: XY = 6 or XY = 6, since XY can not be ve as proved above ..this is sufficient. Statement 2: solve \(X^3*Y = 24\) and \(X^3*Y^2 = 72\) , you will get the value of Y and X. Thus D
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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26 Sep 2010, 01:39
answer is A....explanation: Statement 1 tells that XY =+6 or 6 but it is given that X2*XY is possitive hence XY has to be positive.....2nd statement tells that X is posstive but you can not derive the value of XY.



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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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26 Sep 2010, 01:43
Sorry!! It has to be D Y one can calculate from 2 and Given statement which will tell that XY = 6 and not 6



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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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26 Sep 2010, 01:44
deeplakshya wrote: answer is A....explanation: Statement 1 tells that XY =+6 or 6 but it is given that X2*XY is possitive hence XY has to be positive.....2nd statement tells that X is posstive but you can not derive the value of XY. Statement 2 says X is positive correct the question says \(x^3 *y\) = 24 = positive => only possible when x and y are of same sign =>either ve or +ve since x is positive y will also be positive.
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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26 Sep 2010, 03:42
We are not finding if the answer will be +ve or ve. We need to know the numercial answer.
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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02 Jan 2015, 02:45
If x^3*y = 24, what is the value of x^3*y^3  x^2*y^2?
(1) x^2*y^2 = 36. (2) x^3*y^2 = 72.
From Stmnt.1 we can deduce XY = 6(square of a number can be negative but a square root can't be negative..correct me if am wrong), which will suffice to get unique value for the given question.
From Stmnt.2, here we need to do some substitution: x^3*y^2 = 72 > Y(X^3*Y)=72 > Y(24)=72 > Y=3 If Y=3, X^3*Y=24 >X^3=8 > X=2 With X=2 and Y=3 we will be able to get unique value for the given question.



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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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13 Mar 2016, 10:27
Here is how i went about it \(x^3y=24\) could be \(2^3 3\) or \((2)^3 (3)\) or \(1^3 24\) or \((1)^3 (24)\). question: x^2 y^2 (xy1)= ?? (here the signs of the values dont matter as we can imply they both will have same signs) stmt1: \(x^2 y^2\) = 36. As in x=2 or 2 and y=3 or 3 . Sufficient. stmt2:\(x^3 y^2\) = 72. As in x=2 or 2 and y=3 or 3. Sufficient. Hence D. Let me know if this helps.
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Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2? [#permalink]
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03 Apr 2016, 00:29
I think the trick to this one is recognizing the following:
1.) x^2*y^2 = (x*y)^2 = 36 ==> x*y = 6. We know this has to be positive 6 because of the fact x^3*y = 24. Therefore, sufficient. 2.)x^3*y^2 = 72 = 8*9 = 2^3*3^2. Therefore, x = 2 and y = 3. Sufficient
D is the answer




Re: If x^3*y = 24, what is the value of x^2*y^3  x^2*y^2?
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