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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]

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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.
[Reveal] Spoiler: OA

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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
$$x^3y^3-x^2y^2 = x^3 *y *y^2 - x^2y^2$$

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

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]

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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
$$x^3y^3-x^2y^2 = x^3 *y *y^2 - x^2y^2$$

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

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]

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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
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:
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.

B only !

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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 (xy-1)= ?? (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

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Re: If x^3*y = 24, what is the value of x^2*y^3 - x^2*y^2?   [#permalink] 03 Apr 2016, 00:29
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