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# if x and y are intigers is x^y * y^-x = 1?? 1) x^x > y 2)

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if x and y are intigers is x^y * y^-x = 1?? 1) x^x > y 2) [#permalink]  16 Sep 2006, 03:59
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if x and y are intigers is x^y * y^-x = 1??

1) x^x > y
2) x>y^y
Director
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I used following
A) X^X=Y then stem is =1 but since it is inequality, then it is not = to 1
IMO it should be D
SVP
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For me, it's (B)

Statment 1:
If x = y = 2, then :
> 2^2 = 4 > 2
> 2^2 / (2^2) = 1

If x = 2 and y = 1, then :
> 2^2 = 4 > 1
> 2^1 / (1^2) = 2

INSUFF

Statment 2:
x > y^y thus x > y (x & y are integers) that means x != y

Hence, x^y * y^-x != 1

SUFF
VP
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Re: Excellent iniquality DS [#permalink]  16 Sep 2006, 06:23
yezz wrote:
if x and y are intigers is x^y * y^-x = 1??

1) x^x > y
2) x>y^y

Can some one see if my working is correct?

given x,y are ints

is x^y * y^-x = 1

or x^y / y^x = 1 ===> x^y = y^x

taking logs on both sides we have to prove (y/x)(logx/logy)=1

from (1) we have
xlogx > log y

logx/logy > 1/x

(so we do not know anything about it)

from (2) we have

x>y^y ==> logx > ylogy
Means
logx/logy > y

Then I am lost...
Director
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Hallo trivikram
think that ; or x^y / y^x = 1 ===> x^y = y^x
is NOT correct .It should be (x^y-y^x)/y^x=0 where y^x can not be 0 since division by 0 is not defined
VP
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BG wrote:
Hallo trivikram
think that ; or x^y / y^x = 1 ===> x^y = y^x
is NOT correct .It should be (x^y-y^x)/y^x=0 where y^x can not be 0 since division by 0 is not defined

But BG from there how do we proceed?
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Re: Excellent iniquality DS [#permalink]  16 Sep 2006, 07:37
yezz wrote:
if x and y are intigers is x^y * y^-x = 1??

1) x^x > y
2) x>y^y

The condition x^y * y^-x = 1 will be valid only if x and y are 2 and 4

from statement 2 we can say that, that is not the case. Hence B is the anwer.
_________________

The path is long, but self-surrender makes it short;
the way is difficult, but perfect trust makes it easy.

Senior Manager
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.........................
SVP
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Kudos [?]: 102 [0], given: 0

mailtheguru wrote:
.........................

What's going on ?
Current Student
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for me B is sufficient...

X and Y are integers... we dont know if they are postive or negative...

x^y * y^-x=1?

(1) x^x>y

well say if x and y=2...then 2^2>2...

2^2*1/(2^2)=1; x=2, y=3 then the stem isnt equal to 1

(2)
x>y^y; so we know that |x|>|y| and they are not equal..therefore the stem will never be 1....

sufficient
Senior Manager
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Fig wrote:
mailtheguru wrote:
.........................

What's going on ?

Got screwed
SVP
Joined: 01 May 2006
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mailtheguru wrote:
Fig wrote:
mailtheguru wrote:
.........................

What's going on ?

Got screwed

It's one part of the joy of Maths (or DS? ).... One time u another time someone else (this rule works with me as well )
Senior Manager
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Fig wrote:
mailtheguru wrote:
Fig wrote:
mailtheguru wrote:
.........................

What's going on ?

Got screwed

It's one part of the joy of Maths (or DS? ).... One time u another time someone else (this rule works with me as well )

yeah, sure.
Where are these questiosn from?
Director
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A very shaky B for me as well...

x^y = y^x
=> ylogx = x logy
=> y/x = logy/logx -- (1)

A# x^x > y
=> xlogx > logy
=> From (1), y/x^2 = logy/xlogx < 1
=> y < x^2

Now, if x=2, we have y = 1, 2, 3... if y = 2 then x^y = y^x, but not in the case of y =1 or 3. Hence not sufficient.

B# x > y^y
=> logx > ylogy
=> from (1), y^2/x = ylogy/logx < 1
=> y^2 < x

Now, if x = 27, we have y = 1, 2, 3, 4 or 5; but the expression in the question does not evaluate to 1 in any of the cases. Hence sufficient.
SVP
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Kudos [?]: 126 [0], given: 39

if x and y are intigers is x^y * y^-x = 1??

1) x^x > y
2) x>y^y

rephrase stem x^y *1/y^x = 1 ie: receprocals

This is only possible if x^y = y^x and in turn this is only possible if x=y or x,y belongs to the set {2,4}

from one

x^x > y thus sure x,y are not equall one

x,y could be anything and could be x=4 and y=2 .....insuff

from two

x>y^ythus sure x,y are not equall one and sure /x/> /y/ thus if they are 2,4 x must be the 4 and thus y^y = 4....suff

because now we are sure that the only two conditions that make the assumption true are not valid ( being one or {2,4})

suff

answer is not a shaky b it is B

Last edited by yezz on 16 Sep 2006, 12:35, edited 2 times in total.
SVP
Joined: 01 May 2006
Posts: 1798
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Kudos [?]: 102 [0], given: 0

yezz wrote:
if x and y are intigers is x^y * y^-x = 1??

1) x^x > y
2) x>y^y

rephrase stem x^y *1/y^x = 1 ie: receprocals

This is only possible if x^y = y^x and in turn this is only possible if x=y=1

or x,y belongs to the set {2,4}

from one

x^x > y thus sure x,y are not equall one

x,y could be anything and could be x=4 and y=2 .....insuff

from two

x>y^ythus sure x,y are not equall one and sure /x/> /y/ thus if they are 2,4 x must be the 4 and thus y^y = 4....suff

because now we are sure that the only two conditions that make the assumption true are not valid ( being one or {2,4})

suff

answer is not a shaky b it is B

Not agree with the bold

x = y makes it and no restricted values on it apart 0^0 (recently identified as not fitted for GMAT )
SVP
Joined: 05 Jul 2006
Posts: 1516
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Kudos [?]: 126 [0], given: 39

come on Fig you ve got to get over this exponent DS ...

and i agree with you on your comment but still it would be insuff

I will edit it
SVP
Joined: 01 May 2006
Posts: 1798
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Kudos [?]: 102 [0], given: 0

It's the end of my day here I'm allowed to turn the end of my post to something funny for those who know it
SVP
Joined: 05 Jul 2006
Posts: 1516
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Kudos [?]: 126 [0], given: 39

Man GMAT is funny

funny wn we do silly mistakes " kinder garten ones" apart from the test

and funny when you laugh yourself to death infront of a hard DS that you ve no clue about

we need those jokes all the time

by the way i like your audi
SVP
Joined: 01 May 2006
Posts: 1798
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Kudos [?]: 102 [0], given: 0

Ahhh If u start to speak about Audi... I'm not ready to make an end to this day finally

Frankly, I recommand this brand over the 2 other major german brands But I try to convince no one

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