another algebraic question-having trouble

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coolgirl26: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Tue Mar 03, 2009 1:24 pm

by coolgirl26 » Sun Apr 19, 2009 12:10 pm

IF X^3Y= 24 what is value of X^3Y^3-X^2Y^2

1) X^2Y^2= 36

2) X^3Y^2= 72

Answer B..

I'm having a lot of trouble answering this

how would I just solve for the equation above if it was presented in problem solving form

can someone help asap

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Source: Beat The GMAT — Data Sufficiency | Sun Apr 19, 2009 12:10 pm

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Sun Apr 19, 2009 12:28 pm

x^3 * y^3 - x^2 * y^2 = x^2 * y^2 (xy - 1) = (xy)^2 * (xy - 1).

Now let's get to the stmts:

1. x^2*y^2 = 36 means that xy has two possible values: -6 and 6. This is why you can't use this stmt: it yields two cases. So 1 isn't enough.

2. x^3 * y^2 = 72 means that you can identify y: since x^3 * y = 24 and x^3 * y^2 = 72, y will be the rapport of the two:

y = 72/24 = 3.

Now, since y = 3, this makes x^3 = 24/3 = 8 and there's obviously no other x than 2. Since you get unique values for x (2) and y (3), finding out the value of that long thing in the beginning won't be a problem. This is why 2 is enough.

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