eaakbari wrote:IMO E. But the method of picking numbers took way too long. Can someone suggest alternate approach

Is a/b < 1/2 ?
from the question: is 2a <b ?

statement 1)
2a+1<b

fibbonnaci wrote:oops sorry i missed that..


we need to answer whether a/b < 0.5

statement 1:
a/(b-1) <1/2

if b is positive, (b-1)<b
if a/(b-1) is less than half then a number with greater denominator b should definitely give less than half(coz the numerators are the same).

you can check by plugging in numbers.
say a=1 and b=4,
a/(b-1) = 1/3 which is less than 1/2.
then a/b= 1/4 which is less than 0.5

Now consider b is negative and a is also negative.
say a= -1 and b= -2
then according to the equation a/(b-1) = 1/3 which is less than 1/2,
but a/b= 1/2 which is equal to half.
Therefore insufficient.

Statement 2:
(a-1)/b <0.5
say a= 2 and b= 3
then 1/3< 1/2 but a/b > 1/2.

lets check another value: a=3 and b=6
2/6 < 1/2 but a/b= 1/2. Thus insufficient.

combining both:
we need to plug in numbers that satisfy both the equations
say a=1 and b=4
then a/b<1/2

similarly say a=-1 and b= -5
then too a/b <1/2.

sufficient.