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gopinathhyd
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Can you please clarify these parts? Is it x^2*y or x^(2y)?gopinathhyd wrote:Is X<Y
1. X^2Y = 8
2. Y^2X = 8
Exponents and equations
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Source: Beat The GMAT — Data Sufficiency |
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sanju09
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I assume it's thisgopinathhyd wrote:Is X<Y
1. X^2Y = 8
2. Y^2X = 8
Is X < Y?
1. (X^2) Y = 8.
2. (Y^2) X = 8.
1. (X^2) Y = 8 is possible if X < Y (X = 1, Y = 8), and also if X > Y (X = 4, Y = ½), insufficient.
2. (Y^2) X = 8 is possible if X > Y (X = 8, Y = 1), and also if X < Y (X = ½, Y = 4), insufficient.
Taking together, [(X^2) Y]/ [(Y^2) X] = 1, or X = Y. Hence [spoiler]NO, sufficient
Take C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
As explained above 1 is insufficient, similarly 2 is insufficient
If we take (1)+(2)
then
x^2.y=y^2.x=8
lets take
x^2.y=y^2.x
=>x^2y-x.y^2=0
=>xy(x-y)=0
=>xy=0 or (x-y)=0
=> either x=0 or y=0 or both....(case1)
or
(x-y)=0...(case 2)
Since case 1 is not possible ..because x^2.y=8 or x.y^2=8, not zero
Hence
x-y=0
=>x=y
So c is sufficient to decide
Answer:(C)
If we take (1)+(2)
then
x^2.y=y^2.x=8
lets take
x^2.y=y^2.x
=>x^2y-x.y^2=0
=>xy(x-y)=0
=>xy=0 or (x-y)=0
=> either x=0 or y=0 or both....(case1)
or
(x-y)=0...(case 2)
Since case 1 is not possible ..because x^2.y=8 or x.y^2=8, not zero
Hence
x-y=0
=>x=y
So c is sufficient to decide
Answer:(C)
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gopinathhyd
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sanju09
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Either way, the answer remains same. Taking 1 & 2 together, it's a big [spoiler]YES! Hence C[/spoiler]gopinathhyd wrote:I am sorry,
The correct question is
Is X = Y?
1. (X^2) Y = 8.
2. (Y^2) X = 8.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
