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# Which one of (a^-1+b^-1)^-1 and (a^-1*b^-1)^-1 is greater?

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Senior Manager
Joined: 10 Dec 2004
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Which one of (a^-1+b^-1)^-1 and (a^-1*b^-1)^-1 is greater? [#permalink]  02 Feb 2005, 09:46
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Which one of (a^-1+b^-1)^-1 and (a^-1*b^-1)^-1 is greater?
1) a=2b
2) a+b>1
Manager
Joined: 11 Jan 2005
Posts: 101
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Kudos [?]: 0 [0], given: 0

we simplify the expressions :

from (a^-1+b^-1)^-1
to ab/(a+b)

from (a^-1*b^-1)^-1
to ab

i. not sufficient if a=2b only
we have : (2/3) * b & 2b^2 if 0<b<1 & if b>1 gives different solutions

ii. not sufficient if a+b>1
ab can be negative or positive according to a or b, then we duno

together : if a+b>1 & a=2b then a & b are positive
but we still duno if a or b are between 0 & 1 then no sufficient

E
Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston
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should be C [#permalink]  04 Feb 2005, 11:12
I just answered it somewhere in the forum.
Anirban
should be C   [#permalink] 04 Feb 2005, 11:12
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