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# If X^3Y = 24 , what is the value of X^3Y^3 X^2Y^2 ? (1)

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If X^3Y = 24 , what is the value of X^3Y^3 X^2Y^2 ? (1) [#permalink]  20 Apr 2010, 06:27
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If X^3Y = 24, what is the value of X^3Y^3X^2Y^2?
(1) X^2Y^2 = 36.
(2) X^3Y^2 = 72.
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Re: Good Equation Problem [#permalink]  20 Apr 2010, 07:13
Hussain15 wrote:
If X^3Y = 24, what is the value of X^3Y^3X^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: Good Equation Problem [#permalink]  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: Good Equation Problem [#permalink]  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: Good Equation Problem [#permalink]  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: Good Equation Problem [#permalink]  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: Good Equation Problem [#permalink]  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: Good Equation Problem [#permalink]  26 Sep 2010, 00:39
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: Good Equation Problem [#permalink]  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: Good Equation Problem [#permalink]  26 Sep 2010, 00:44
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: Good Equation Problem [#permalink]  26 Sep 2010, 02:42
We are not finding if the answer will be +ve or -ve.
We need to know the numercial answer.

B only !
Re: Good Equation Problem   [#permalink] 26 Sep 2010, 02:42
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