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Is y^x > x^y?

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Expert Post
Math Expert
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V
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128601 [0], given: 12180

Is y^x > x^y? [#permalink]

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New post 10 Sep 2017, 21:42
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A
B
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D
E

Difficulty:

  55% (hard)

Question Stats:

55% (01:20) correct 45% (01:34) wrong based on 42 sessions

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Kudos [?]: 128601 [0], given: 12180

Senior Manager
Senior Manager
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G
Joined: 02 Jul 2017
Posts: 252

Kudos [?]: 59 [0], given: 59

Location: India
GMAT ToolKit User CAT Tests
Is y^x > x^y? [#permalink]

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New post 10 Sep 2017, 23:14
Is y^x > x^y?

(1) y > x
if y=2 x=1 => 2^1 > 1^ 2 => 2>1 true
y=2 x= -2 => 2^(-2) > (-2)^2 => 1/4 > 2 False
Not sufficient
(2) x is a positive number
so x>0 . Nothing about y.
if y=2 x=1 => 2^1 > 1^ 2 => 2>1 true
if y =-2 x=1 => (-2)^1 > (1)^(-2) => -2 > 1 false
So Not sufficient

1+2
y> x and x>0
( Its not given that numbers are integers so always check for fractions. If given x and y are integers equation might be different)
if y=2 x=1 => 2^1 > 1^ 2 => 2>1 true
y= 1/2 and x=1/4 => (1/2)^(1/4) > (1/4)^(1/2) => (1/2)^(1/4) > 1/2 True ( Well this step not required)
y =5 and x=3 => 5^ 3 > 3^5 => 125 > 243 False
Not Sufficient


Answer: E

Kudos [?]: 59 [0], given: 59

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G
Joined: 26 Mar 2013
Posts: 1258

Kudos [?]: 285 [0], given: 163

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Is y^x > x^y? [#permalink]

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New post 11 Sep 2017, 02:21
Bunuel wrote:
Is y^x > x^y?

(1) y > x
(2) x is a positive number


(1) y > x

Let y=2 & x =1.........2^1 > 1^2...........Answer is yes

Let y=4 & x =3.........4^3 > 3^4...........Answer is NO

Insufficient

(2) x is a positive number

Same examples above

Insufficient

Combine 1 & 2

Same examples above

Insufficient

Answer: E

Kudos [?]: 285 [0], given: 163

Is y^x > x^y?   [#permalink] 11 Sep 2017, 02:21
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