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Source: Beat The GMAT — Data Sufficiency |
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cramya
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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)
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)
Last edited by cramya on Sun Jan 04, 2009 12:51 am, edited 2 times in total.
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logitech
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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)
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)
Last edited by logitech on Sun Jan 04, 2009 1:56 am, edited 1 time in total.
LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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pandeyvineet24
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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 ?
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 ?
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
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
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cramya
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U r absolutely correct. Good catch.IMO: D
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.
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.
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.
cramya wrote:y^2 = y*yx^3y^2 = 72 -------- Step-I
(x^3y)(y) = 72 ------ Step-II
how did we reach from first step to second
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.
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pandeyvineet24
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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...
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.pandeyvineet24 wrote: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...
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The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.
