Square and Cube

[kuiper]

If X^3 * Y = 24

What is the value of (X^3 * Y^3 - X^2 * Y^2)?

A. X^2 * Y^2 = 36

B. X^3 * Y^2 = 72

For some reason OA is given as B I found it to be D



Because in B - dividing the equation with given equation in the problem we can find the value of Y and then X

In A, dividing the equation with given equation in the problem we get Y/X = 3/2. From this we get Y = 3X/2 and substitute in back in any equation we get X = 2 and can be found.

Did I make a mistake or is the OA incorrect?

[Rahul@gurome]

What you are doing, is definitely giving us that y = 3x/2.
Substituting this in the main equation we get x^4 = 16.
This gives 2 values of x, x = 2 and x = -2.
For these two values of x, we get different values of the expression (X^3 * Y^3 - X^2 * Y^2).
So A. alone is not sufficient.

[TOPGMAT]

Hi Kuiper,

Ans is B...
If you find yourself with such ans choices, be careful..

stmt1: x=-2 and y=-3 = 36 and x=-2 and y= -3 ==> 24.... Both are satisfied..
x=2 and y=3 ==>36 and x=2 and y=3 => 24..
Therfore x,y can be (-2,-3) and (2,3)... Not sufficient.

stmt2: x^3 should be positive... Hence x,y = 2,3 only... Hence sufficient.

[kuiper]

Thank you Rahul and TOPGmat

Appreciate your help