877. Traveling the back roads of Hungary, in 1905 Béla Bartók and Zoltán Kodály began their pioneering work in ethnomusicology, and they were armed only with an Edison phonograph and insatiable curiosity.

(A) Traveling the back roads of Hungary, in 1905 Béla Bartók and Zoltán Kodály began their pioneering work in ethnomusicology, and they were armed only
(B) In 1905, Béla Bartók and Zoltán Kodály, traveling the back roads of Hungary, began their pioneering work in ethnomusicology, and they were only armed
(C) In 1905 Béla Bartók and Zoltán Kodály began their pioneering work in ethnomusicology, traveling the back roads of Hungary armed only
(D) Having traveled the back roads of Hungary, in 1905 Béla Bartók and Zoltán Kodály began their pioneering work in ethnomusicology; they were only armed
(E) Béla Bartók and Zoltán Kodály, in 1905 began their pioneering work in ethnomusicology, traveling the back roads of Hungary, arming themselves only

Solution:

Pronoun + Tense

In A and B, the antecedent of “they” is not clear and hence, both the choices are incorrect.

In D, “having traveled” changes the meaning. It suggests that “they began their pioneering work..” after traveling where as the intended meaning is that “they began…work..” while “traveling..”.

In E, “arming themselves” suggest that they went on arming themselves while traveling. Wrong tense. Hence, E is incorrect.
In C, there is no ambiguous “they” and sentence is concise. Hence, C is the best choice.