ii |x-3| is not equal to zero
lets take statement i. there are four possibles.
a. both modulas are +ve; x = 3.
b. both modulas are -ve; x = 3.
c. |x+1| is +ve and (2|x-1|) is -ve; x = 1/3.
d. |x+1| is -ve and (2|x-1|) is +ve; x = 1/3
so x is either 1/3 or 3. so statement i is not suff.
statement ii says |x-3| = 0. this alone is also not enough cuz we do not know the value of x and only know x is not equal to 3.
from i and ii, both, we know that x = 1/3 which is less tha 1.
So C is answer.