For what percent of those tested for a certain infection was the test

I think this problem goes beyond 2 variables. You can use the overlapping sets table, as there can be 4 possibilities for patient to be infected/not-infected:
Tests are Positive & Accurate -> Patient is infected
Tests are Positive & Inaccurate -> Patient is NOT infected
Tests are Negative & Accurate -> Patient is NOT infected
Tests are Negative & Inaccurate -> Patient is infected

Our objective is to identify the value of cell marked in yellow (i.e. Accurate tests) hence find its ratio to TOTAL tests (i.e. % Accuracy)

(1) Of those who tested positive for the infection,1/8 did not have the infection.
INSUFFICIENT: Refer to the diagram, this gives no info to derive the value for yellow cell (i.e. Accurate tests)
(2) Of those tested for the infection, 90 percent tested negative.
INSUFFICIENT: Refer to the diagram, this gives no info to derive the value for yellow cell (i.e. Accurate tests)

Combining (1) & (2)
INSUFFICIENT: Even after combining the statements are INSUFFICIENT to derive the value for yellow cell (i.e. Accurate tests)

Hence Choice(E) is the answer.