Use "number of equations = number of unknowns", but beware of the twist at the end.

form equations: Let A be the investment in A,
B in B,
p be the interest in A.
thus, the interest in B is 1.5p = p*3/2.
Stat. (1):

thus, 2 equations:
A*p = 50
B*p*(3/2)=150.
(technically should be p/100, but that's not important for our purposes).

2 equations with 3 unknowns is insufficient - you cannot isolate A from these equations.

Stat. (2): B=2A. Alone, this is obviously insufficient to find A - again, one equation, 2 unknowns.

Combined:
we now know that
A*p=50
B*p*3/2 = 150
B=2A

looks fine: 3 equations, 3 unknowns, sufficient, right? Take it a few steps down the line: substitute B=2A in eq.2 to get
A*p=50
2A*p*3/2 = 150
the 2s reduce to leave A*p*3=150 - a recycled version of A*p=50.
So it's not really 3 equations, 3 unknowns - we only have 2 different equations with unknowns, which is why the statements combined are still insufficient. Answer is E.