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

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

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21 Aug 2007, 07:15
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If a and b are positive, is (a^-1 + b^-1)^-1 less than (a^-1*b^-1)^-1?

(1) a = 2b
(2) a + b > 1

It is really difficult for me.

Thank you for help!

BTW oa is B
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21 Aug 2007, 07:30
OK i get B as well..here is how..

the stem simplifys to (ab/(b+a))> ab?

1) a=2b

so we 2b^2/3B > 2b^2?

well if b=1/3 then you gt 2/9=2/9

if b >1/3 then yes ab/(b+a) is less than ab

Insuff

2) a+b>1 well which means ab/(sometheing greater than 1) is < ab

sufficient

B it is...
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21 Aug 2007, 09:52
I got scared initially with the equation as well..But when you simplify it..

ab/ a+b < ab ?

or 1 / a+b <1> 1

So values are 2, 3, 4...

1/2 < 1
1/3 < 1
1/4 < 1

Hence, B is sufficient...
21 Aug 2007, 09:52
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