DS-algebra (tricky!!)

[vscid]

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

question is from gmatscore[/img]

[kylo]

IMO B.



Thanks!

[vscid]

IMO B.



Thanks!

can u show the solution?

[kylo]

(X^3)(Y^2) = 72
24*Y = 72
Y = 3

(X^3)Y = 24
X = 2

hence we can find out the value of (X^3)(Y^3) - (X^2)(Y^2).


Thanks!

[vscid]

(X^3)(Y^2) = 72
24*Y = 72
Y = 3

(X^3)Y = 24
X = 2

hence we can find out the value of (X^3)(Y^3) - (X^2)(Y^2).


Thanks!

for statement 1:

given X^3Y=24, what is the value of X^3Y^3 - X^2Y^2
that is X^2Y^2(XY -1)=?


also X^2Y^2=36
that means (XY)^2=6^2
now XY can be either +6 or -6

from ques we know that X^3Y=24
divide by X^2 (which will always be positive, if x is a real number)
also it is obvious that x and y are not 0
XY=24/x^2, positive number(24) divided by a positive value (X^2), will be positive
that is XY is positive
so XY=6
sufficient

what do you think kylo?

[kylo]

nice work - vscid. man u can really be very creative.

but u r missing few cases here -
(X^2)(Y^2) = 36
case1 X=-1 & Y=6
case2 X=1 & Y=-6

in both the above cases XY will negative.

hope this helps.



Thanks!

[Grv]

I agree the answer is D.

Alt. way to show I is sufficient.
We have x^3 y = 24 ....(A)
I gives us x^2 y^2 = 36 ....(B)

Divide (A) by (B)
x/y = 2/3
=> y = 3x/2 ....(C)

Substitute this in (A).
x^3.(3x/2) = 24
=> x = +/- 2.
if x is + 2, y is +3
if x is -2, y is -3.
In either case xy is +6.

Hence we can evaluate (xy)^3 - (xy)^2.

[kylo]

yup! now i agree with both (vscid & Grv) of u.

the 2 cases above, mentioned in my post, will not hold true for (X^3)Y = 24.

hence IMO D as well.



Thanks!

[michael_shaunn]

well..i believe that the answer can be obtained by using either of the clues..........and even without the clues as well.Given below is how...and its prettty simple...
In the question given is that......x^3*y=24 i.e 2^3*3=24 after prime factorizing 24.
comparing, we get x=2 and y=3.

lets talk about clue 1: x^2*y^2=36=2^2*3^2 which gives x=2 and y=3 or x=3 and y=2.But due to symmetry of the question whatever we choose x to be and the corresponding y,the answer wont change.

lets talk about the clue 2: x^3*y^2=72=2^3*3^2 implies that x=2 and y=3. Hence we obtain the solution.

[JonathanSchneider]

Be careful, Michael. We can't assume that x and y are integers.

Nice work on the solutions above! The trick is indeed in recognizing that becayse (x^3)y = 24, x and y must have the same sign.