None of the conditions supply anything related to exact amount.
so E

in A, we do not know the interest rate so can not find the amount.

B gives one amount in terms of other but total is still missing

I tried to make direct algebraic approach to this

Linda put an amount of money into each of two new investments, A and B, that pay simple annual interest. If the annual rate of investment B is one and a half times that of investment A, what amount did Linda put into investment A?
1. The interest for 1 year is $50 for investment A and $150 for investment B
2. The amount that Linda put into investment B is twice the amount that she put into investment
A

Total (let is be t) = a + b, a=?
We have rate(B) = (3/2) rate a, let rate A be R, so rateB is (3/2)R

(1)
(r/100)a=50, ra=5000
3r/200* * (t-a) = 150
3r * (t-a) = 30000
rt-5000 = 10000
rt = 5000
1 equatin 2 variables
INSUFF

(2)
b=2a, so t=3a
nothing more?
INSUFF

(1)(2)
rt = 5000, t=3a
r*3a = 5000
ra = 5000/3
1 equatin 2 variables
INSUFF

E