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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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17 Sep 2006, 12:00
Fig wrote:
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 )

This looks like a B to me:

Changing the problem stem to logs we have to prove that:
log x/ log y = y/x

From 1:
we get, log x > y/x
since we dont know anything about log y, we cannot proceed from this data.

From 2:
simplifying we get log x /log y > y/x
thus log x /log y does not equal y/x. which proves are requirement.

Hence a B

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