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

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If x^3*y = 24, what is the value of x^2*y^3 - x^2*y^2? [#permalink] New post 20 Apr 2010, 06:27
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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] New post 20 Apr 2010, 07:13
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.

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Re: If x^3*y = 24, what is the value of x^2*y^3 - x^2*y^2? [#permalink] New post 20 Apr 2010, 07:40
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
\(x^3y^3-x^2y^2 = x^3 *y *y^2 - x^2y^2\)

= \(y^2(24-x^2)\)

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] New post 20 Apr 2010, 08:04
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
\(x^3y^3-x^2y^2 = x^3 *y *y^2 - x^2y^2\)

= \(y^2(24-x^2)\)

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] New post 20 Apr 2010, 08:33
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] New post 25 Sep 2010, 01:31
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] New post 25 Sep 2010, 02:08
\(X^3*Y = 24\) => 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] New post 26 Sep 2010, 00:39
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] New post 26 Sep 2010, 00:43
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] New post 26 Sep 2010, 00:44
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] New post 26 Sep 2010, 02:42
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] New post 29 Dec 2014, 07:25
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Re: If x^3*y = 24, what is the value of x^2*y^3 - x^2*y^2? [#permalink] New post 02 Jan 2015, 01:45
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.
Re: If x^3*y = 24, what is the value of x^2*y^3 - x^2*y^2?   [#permalink] 02 Jan 2015, 01:45
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