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# x and y are positive integers, is X^y <= Y^x? 1. X = y^2

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Senior Manager
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x and y are positive integers, is X^y <= Y^x? 1. X = y^2 [#permalink]

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14 Aug 2006, 23:05
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x and y are positive integers, is X^y <= Y^x?

1. X = y^2

2. X = 2y

Not sure about the OA, let's discuss guys.
CEO
Joined: 20 Nov 2005
Posts: 2896
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 25

Kudos [?]: 291 [0], given: 0

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14 Aug 2006, 23:54
I think this is A

St1:
x--------y-----------ANSWER
25------5-----------YES
1--------1----------YES
4--------2----------YES
SUFF

St2:
x--------y-----------ANSWER
8--------4----------YES
2--------1----------NO
1--------1-----------YES
INSUFF
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

GMAT Instructor
Joined: 04 Jul 2006
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Kudos [?]: 307 [0], given: 0

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15 Aug 2006, 01:06
x and y are positive integers, is X^y <= Y^x?

1. X = y^2

2. X = 2y

With (1) LS= y^(2y) RS= y^(y^2)

If y=1, LS=RS=1, and if y is at least 2, y^2-2y=y(y-2)>=0, so y^2>=2y and RS>=LS

Suff

With (2) LS= (2y)^y RS= y^(2y)=(y^2)^y

Here if y=1 LS=2>1=RS, but if y=2, LS=RS=16

Not suff
Manager
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Location: Philadelphia
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15 Aug 2006, 12:09
I think this is A
Quote:
St1:
x--------y-----------ANSWER
25------5-----------YES
1--------1----------YES
4--------2----------YES
SUFF

St2:
x--------y-----------ANSWER
8--------4----------YES
2--------1----------NO
1--------1-----------YES
INSUFF
_________________

I concur... A it is
Manager
Joined: 20 Mar 2006
Posts: 200
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Re: DS: X^y <= Y^x [#permalink]

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17 Aug 2006, 21:17
M8 wrote:
x and y are positive integers, is X^y <= Y^x?

1. X = y^2

2. X = 2y

Not sure about the OA, let's discuss guys.

x,y={I,+}
(1) x=4 y=2 Yes
x=1, y=1 yes
x=9, y = 3 yes
x=100, y =10 yes

AD

(2) x=2 y =1 No
x=4 y=2 Yes

Hence A

Heman
Re: DS: X^y <= Y^x   [#permalink] 17 Aug 2006, 21:17
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# x and y are positive integers, is X^y <= Y^x? 1. X = y^2

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