IMO B
In statement 1 ;
replacing value of a=2b
the left hand side = 2b/3
and the right hand side = 2b^2
if 0<b < 1 => b^2 < b and
if b > 1 => b^2 b
So , the information is insufficient
In statement 2 ;
we know that a+b>1
simplifying the L.H.S(left hand side) of the inequality , we get ab/a+b
and the R.H.S is ab
we know that ab is positive and dividing ab by a number greater than 1 (since a+b >1) will result in a number lesser than ab
So L.H.S< R.H.S
So , it is sufficient
Roots
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(a^-1+b^-1)^-1=ab/a+b..and (a^-1*b^-1)^-1=ab
so the question is whether (ab/a+b)<ab
from 1 a=2b
hence ab=2b^2..and a+b=3b
ab/a+b=2/3b..this may or may not be greater that 2b^2 or ab--->not sufficient
from 2,
a+b>1 or 1>1/a+b..or ab>ab/a+b--->sufficient
Ans option B
so the question is whether (ab/a+b)<ab
from 1 a=2b
hence ab=2b^2..and a+b=3b
ab/a+b=2/3b..this may or may not be greater that 2b^2 or ab--->not sufficient
from 2,
a+b>1 or 1>1/a+b..or ab>ab/a+b--->sufficient
Ans option B
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