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# Is x>y? (1). x^2>2y (2). x^3>y^4

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Is x>y? (1). x^2>2y (2). x^3>y^4 [#permalink]

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03 Oct 2004, 07:15
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Is x>y?

(1). x^2>2y

(2). x^3>y^4
Joined: 31 Dec 1969
Location: Russian Federation
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
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GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)
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03 Oct 2004, 07:56
1. X^2-2y>0. if x=2 and y =1 then X>Y. However if x=-2 and y=1, X<Y, but satifies the equation 1 - and cant say x > y or not. Hence Insufficient.

2. X^3-Y^4 >0. Y^4 is always +ve. X^3 can be +ve or -ve. It has to be larger than Y^4 to satisfy the equation. So X>Y always. Sufficient.

Hence B
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03 Oct 2004, 08:11
Anonymous wrote:
1. X^2-2y>0. if x=2 and y =1 then X>Y. However if x=-2 and y=1, X<Y, but satifies the equation 1 - and cant say x > y or not. Hence Insufficient.

2. X^3-Y^4 >0. Y^4 is always +ve. X^3 can be +ve or -ve. It has to be larger than Y^4 to satisfy the equation. So X>Y always. Sufficient.

Hence B

I would take a C.

statement 2 : what about x = 0.4 y = 0.5
x^3 > y^4 but is x > y ..No
The 3 cases to be considered are negativity, (0,1) range and > 1 range
Combine both
x^5 >2y^5 hence x>y.
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Franky
http://franky4gmat.blogspot.com

Joined: 31 Dec 1969
Location: Russian Federation
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)
Followers: 0

Kudos [?]: 233 [0], given: 104566

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03 Oct 2004, 09:40
agree with B.myfrankenstein note that 4/10*3 is not bigger than 5/10*3.
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03 Oct 2004, 10:12
1) Insufficient. Easy to see.

2) We can infer that X>0 and moreover:

if x>=1 then y<1. So X>Y.
if 0<x<1 then y could be negative or 0<y<1.
Y could be > X. Consider x=1/4, y=3/4.
B is out.

1,2) I couldn't reach any other conclusion so i pick E.
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03 Oct 2004, 10:26
Anonymous wrote:
agree with B.myfrankenstein note that 4/10*3 is not bigger than 5/10*3.

it is not multiplication , it's raised to...
x = 0.4 ; y = 0.5
x^3 = .064 ; y^4 = (.0625)

x^3 > y^4 but as yu can see x< y.
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Franky
http://franky4gmat.blogspot.com

03 Oct 2004, 10:26
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