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[vscid]

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

[cramya]

I am getting B)

[logitech]

I am getting B)

Good for you Cramya!

[cramya]

Given: X^3Y = 24

To find: x^3y^3 - x^2y^2

Stmt II

x^3y=24

x^3y^2 = 72
(x^3y)(y) = 72
24y=72
y=3

x^3y=24
x^3*3 = 24

x^3 = 8

x has to be 2

One definite value for x^3y^3 - x^2y^2

SUFF

Stmt I
X^3Y = 24

X^2Y^2 = 36
Multiply by x on both sides

x^3y^2 = 36x
(x^3y) y = 36x
24y=36x
x/y = 2/3
3x = 2y

X^2Y^2 = 36
x^2*(3x/2)^2 = 36
x^4 = 36*4 / 9

x^4=16

x could be 2 or -2

If x is positive y is positive and if x is negative y is negative and x^3y^3 values will be the same either way.

One definite value

SUFF

Choose D)

[logitech]

EDITED

If X^3Y = 24, what is the value of X^3Y^3 - X^2Y^2 ?

1] X^2Y^2 = 36 MEANS XY=6

X^3Y = 24 so..X^2=4 --X=2 or -2 And Y =3 or -3

So we can actually FIND

SUFF

2] X^3Y^2 = 72 and X^3Y = 24 so, Y=3 and X =2

So you can calculate X^3Y^3 - X^2Y^2 ? ( but please don't)

[anabbasi]

x^3y^2 = 72 -------- Step-I
(x^3y)(y) = 72 ------ Step-II

how did we reach from first step to second

[cramya]

x^3y^2 = 72 -------- Step-I
(x^3y)(y) = 72 ------ Step-II

how did we reach from first step to second

y^2 = y*y

We are borrowing one of the y's to form x^3y since we have a value for it given in the problem (24)

[pandeyvineet24]

Why do we need to calculate X and Y.

I think A should be sueffcient

If X^3Y = 24, what is the value of X^3Y^3 - X^2Y^2 ?

1] X^2Y^2 = 36

X^3Y^3 - X^2Y^2 = 24^3 - 36 = 13788

Stmt 1 should be sueffcient as well.

Did i miss anything ?

[cramya]

X^3Y^3 - X^2Y^2 = 24^3 - 36 = 13788

x^3y = 24 and x^3Y^3 is not 24

Hence we find one definite value for x and y

Hope this helps!

[mental]

IMO: D

well statement 2 is sufficient.

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

[cramya]

IMO: D

U r absolutely correct. Good catch.

I was too quick to jump in to a conclusion with 2 different values for x. i.e wihtout evaluating x^3y^3-x^2y^2 expression to see if it gave 2 different answers

Stmt I
X^3Y = 24

X^2Y^2 = 36
Multiply by x on both sides

x^3y^2 = 36x
(x^3y) y = 36x
24y=36x
x/y = 2/3
3x = 2y

X^2Y^2 = 36
x^2*(3x/2)^2 = 36
x^4 = 36*4 / 9

x^4=16

x could be 2 or -2

If x is positive y is positive and if x is negative y is negative but x^3y^3 values will be the same either way.

One definite value

SUFF


The answer indeed would be D).

I have adjusted my post above.

[rajataga]

damnnnnnnn, we need brackets when posting indices..

i had to go through all the posts, just to figure out if it was (X^3y) which was squared, or (3y) or just y....


PS: im still not sure which one it is, although cramya's post indicate that just y is raised to 2.

[rajataga]

x^3y^2 = 72 -------- Step-I
(x^3y)(y) = 72 ------ Step-II

how did we reach from first step to second

y^2 = y*y

We are borrowing one of the y's to form x^3y since we have a value for it given in the problem (24)

i am not sure if we can do this...

cause by this u mean,

x^3y^2 = (x^3y)(y)

substitute, x=2, y=2 in this, and this does not hold true.

[pandeyvineet24]

agree with rajat..its very confusing without the brackets.
i interpreted X^3Y^3 as X raised to power 3Y raised to power 3. which equals X raised to 9Y.
by the look of statement it appeared that way...

[vscid]

agree with rajat..its very confusing without the brackets.
i interpreted X^3Y^3 as X raised to power 3Y raised to power 3. which equals X raised to 9Y.
by the look of statement it appeared that way...

Please check attachment.