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

Question

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

buffdaddy · Answer

the question reads
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

bsd_lover · Answer

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.

domleon · Answer

question to our experts: can anyone tell me why A is not sufficient?

cheers

buffdaddy · Answer

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

pmenon · Answer

i said E because although stem says positive numbers, it doesnt mention that they have to be positive INTEGERS ...

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