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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.

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.

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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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.

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