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# If a and b are positive, is (a^-1 + b^-1)^-1 less than

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Manager
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If a and b are positive, is (a^-1 + b^-1)^-1 less than [#permalink]

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07 Nov 2006, 11:51
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If a and b are positive, is (a^-1 + b^-1)^-1 less than (a^-1b^-1)^-1?
(1) a = 2b
(2) a + b > 1

Last edited by girikorat on 07 Nov 2006, 12:08, edited 1 time in total.
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07 Nov 2006, 12:03
(a-1b-1)-1, I understand it as (a-b-1)-1...

o (a-1 + b-1)-1 = a + b -3
o (a-1b-1)-1 = a - b -2

a + b -3 < a - b -2 ?
<=> 2*b < 1
<=> b < 1/2 ?

From 1:
a=2b.... Brings nothing about a limit of b.

INSUFF.

From 2:
a+b>1
o if b=1/4 and a=1 >>> b < 1/2
o if b=1 and a=1 >>> b > 1/2

INSUFF.

Combining (1) and (2)

a + b > 1
<=> 2b + b > 1
<=> b > 1/3 so could still be either > 1/2 or < 1/2.

INSUFF.
Senior Manager
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07 Nov 2006, 12:07
Considering Fig's formatted question answer is E
Manager
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07 Nov 2006, 12:09
Copied some of these Questions from a pdf...didn't bother to check the formatting.. I have corrected the Question stem ...please look into it now.
Senior Manager
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07 Nov 2006, 12:15
The question simplies to is a+b>1

1 a=2b thus a+b=3b now 3b may or maynot be greater than 1 insuff
2 suff
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08 Nov 2006, 16:31
How does this simplify to a+b > 1??

I get:

(a^-1 + b^1)^-1 = 1/(1/a +1/b) = a+b

and

(a^-1*b^-1)^-1 = 1/(1/a * 1/b) = ab

Simplifying to is a+b < ab????
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08 Nov 2006, 18:26
How does this simplify to a+b > 1??

I get:

(a^-1 + b^1)^-1 = 1/(1/a +1/b) = a+b

and

(a^-1*b^-1)^-1 = 1/(1/a * 1/b) = ab

Simplifying to is a+b < ab????

hey. your first one is wrong. look at it carefully.
08 Nov 2006, 18:26
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