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# Is x^y less than or equal to y^x?

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Intern
Joined: 23 Aug 2009
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Is x^y less than or equal to y^x?  [#permalink]

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22 Sep 2011, 07:39
4
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:25) correct 57% (02:30) wrong based on 126 sessions

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Is x^y less than or equal to y^x?

(1) x^(1/2) = y
(2) x = 2y
Intern
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Joined: 19 Nov 2010
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Re: Is x^y less than or equal to y^x  [#permalink]

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22 Sep 2011, 08:04
C.

1. X= y^2 (doesn't Hek=lp)
2. X=2y (Doesn't help by itself)

but when we use both.. 2y=Y^2 thus Y=2... now we can solve!

So C!
Manager
Joined: 20 Aug 2011
Posts: 121
Re: Is x^y less than or equal to y^x  [#permalink]

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22 Sep 2011, 23:01
Are you sure this question is correct?

Y can also be zero if you combine statements 1 & 2.
Y= 0 or 2.
The form can be 0^0 & this form is undefined.
Does the question specify that both x & y are positive/non-zero?
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Re: Is x^y less than or equal to y^x  [#permalink]

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23 Sep 2011, 03:43
I also got two different set of values.
Manager
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Re: Is x^y less than or equal to y^x  [#permalink]

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29 Sep 2011, 07:29
1
zura wrote:
Is x^y less than or equal to y^x?

1) rootx=y

2) x=2y

A tough question. Took 3 mins to solve

1. x = y^2
Means and y are +ve

Case 1:
x = 0.01, y =0.1
with these values x^y > y^x

Case 2 : x = y =1
with these values x^y = y^x

Case 3: x = 4, y =2
with these values x^y = y^x

Case 4: x = 9, y =3
with these values x^y < y^x

So Insufficient

2) x = 2y
Insufficient

3) Combininng we get only one option
x = 4, y =2, in which x^y = y^x
Sufficient, hence (C)
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Re: Is x^y less than or equal to y^x  [#permalink]

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29 Sep 2011, 08:02
When the 2 statements are taken together -
i.e x=y^2 and x=2y, we get
y^2 = 2y
y^2 - 2y=0
y(y-2)=0

Therefore y=0 or y=2
Clearly it creates 2 different answers for the the inequality.
I believe (E) should be the answer
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Re: Is x^y less than or equal to y^x  [#permalink]

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29 Sep 2011, 09:51
braxus wrote:
When the 2 statements are taken together -
i.e x=y^2 and x=2y, we get
y^2 = 2y
y^2 - 2y=0
y(y-2)=0

Therefore y=0 or y=2
Clearly it creates 2 different answers for the the inequality.
I believe (E) should be the answer

For y=0, x=0
0^0 = 0^0

For y=2, x = 4
2^4 = 16 = 4^2

Hence (C)
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Re: Is x^y less than or equal to y^x  [#permalink]

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03 Oct 2011, 02:23
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Re: Is x^y less than or equal to y^x  [#permalink]

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05 Oct 2011, 03:44
braxus wrote:
When the 2 statements are taken together -
i.e x=y^2 and x=2y, we get
y^2 = 2y
y^2 - 2y=0
y(y-2)=0

Therefore y=0 or y=2
Clearly it creates 2 different answers for the the inequality.
I believe (E) should be the answer

On solving this, you do get two different values for y. But variables cannot take values which make an expression undefined e.g. given y/x, x cannot be 0 since division by 0 is not allowed. Given x^y, both x and y cannot be 0 since 0^0 is not defined. Hence y will not take the value 0. y must be 2 only.
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Re: Is x^y less than or equal to y^x?  [#permalink]

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12 Aug 2018, 16:56
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Re: Is x^y less than or equal to y^x?   [#permalink] 12 Aug 2018, 16:56
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