The first split is "that/with". If that is not easy elimination - look at the meaning. The sentence says that chest cold gravely "strain" the voice.
Marian Corey has developed a chest cold
that, with persistent coughing, could gravely strain the five-octave voice that earned her fame.
A. that, [strike]with persistent coughing[/strike], could gravely strain
D - out for passive "be"
E - change of meaning. Looks like Corey "strain" her own voice. Illogical.
MeinKampf
Marian Corey has developed a chest cold that, with persistent coughing, could gravely strain the five-octave voice that earned her fame.
A. that, with persistent coughing, could gravely strain
B. that, because of persistent coughing, could be a grave strain for
C. with persistent coughing, and it could gravely strain
D. with persistent coughing and could be a grave strain for
E. with persistent coughing and could gravely strain
First, I eliminated answer choices with "could be a grave strain for"...diction...B and D gone.
Then I eliminated C, "it" is not required for the subject.
I got confused between A and E, but selected E.
Could you please explain your answers.