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

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Senior Manager
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If a and b are positive, is (a^-1+b^-1)^-1 less than (a^-1 [#permalink]  11 Jun 2008, 23:05
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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
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Director
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Re: DS question [#permalink]  12 Jun 2008, 01:14
vdhawan1 wrote:
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

is $$\frac{1}{\frac{1}{a}+\frac{1}{b}} < ab$$

which can be simplified to is b+a > 1

as seen 1) is insufficient and 2) is sufficient
CEO
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Re: DS question [#permalink]  12 Jun 2008, 01:28
Hi
$$\frac{1}{\frac{1}{a}+\frac{1}{b}} < ab$$

simplifies to
$$\frac{ab}{a+b} < ab$$
since $$a$$ and $$b$$ are positive we can safely multiply both sides by $$ab$$ and $$a+b$$

Hence it can be simplified to

$$a+b>1$$

B is sufficient.
Manager
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Re: DS question [#permalink]  12 Jun 2008, 01:36
question to our experts: can anyone tell me why A is not sufficient?

cheers
Director
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Re: DS question [#permalink]  12 Jun 2008, 01:42
domleon wrote:
question to our experts: can anyone tell me why A is not sufficient?

cheers

after you simplify the question, it simplifies to is a+b > 1 ?

the stem says a and b are both positive, but it doesnt say that they are integers

so lets say if a=0.4 and b = 0.2 a+b < 1
but if a=6 and b = 3 a+b > 1

so 1) isn't sufficient
SVP
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Re: DS question [#permalink]  12 Jun 2008, 03:52
i said E because although stem says positive numbers, it doesnt mention that they have to be positive INTEGERS ...
Re: DS question   [#permalink] 12 Jun 2008, 03:52
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