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# Is x^y >y^x? 1) x^(1/2)=y 2) x=2y

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Is x^y >y^x? 1) x^(1/2)=y 2) x=2y [#permalink]  02 Sep 2006, 23:05
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Is x^y >y^x?

1) x^(1/2)=y

2) x=2y
Senior Manager
Joined: 14 Jul 2005
Posts: 402
Followers: 1

Kudos [?]: 12 [0], given: 0

Re: DS Inequality with exponents [#permalink]  02 Sep 2006, 23:55
apollo168 wrote:
Is x^y >y^x?

1) x^(1/2)=y

2) x=2y

Seems like C

From 1, sqrt(x) = y i.e. say x=0,1,4,9,16 etc... then y=0,1,2,3,4 etc..

for x,y=1 1>1 is false
for x=4,y=2 16>16 is false
for x=9,y=3 9^3 > 3^9 is also false

But for x=1/4, y =1/2 then 1/4^1/2 > 1/2^1/4

Hence INSUFF

From 2, x=2y i.e y=1, x=2

for y>1/2 the stem is true
for y<1/2 the stem is false (y=1/4, x=1/2)

hence INSUFF

Combined we get x^1/2 = x/2
i.e. 2 * x^1/2 = x

squaring 4x = x^2
x(x-4) = 0

i.e. x=0 or x=4

In both cases the values on both sides are equal hence SUFF
Re: DS Inequality with exponents   [#permalink] 02 Sep 2006, 23:55
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# Is x^y >y^x? 1) x^(1/2)=y 2) x=2y

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