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Is y^x > x^y?

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Joined: 02 Sep 2009
Posts: 46284
Is y^x > x^y? [#permalink]

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New post 10 Sep 2017, 21:42
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (01:15) correct 44% (01:28) wrong based on 52 sessions

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GMAT 1: 730 Q50 V38
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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
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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
Is y^x > x^y?   [#permalink] 11 Sep 2017, 02:21
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