I think what has been tripping up most people is the use of whose. whose – can modify people or things.
Also - you can solve this problem by the process of elimination.
1) Remove the fluff -
The capital of Bosnia-Herzegovina, Sarajevo’s population was 51,9192) Check each answer
sacmanitin wrote:
(A) Bosnia-Herzegovina, Sarajevo’s population
- Sarajevo’s population is NOT the capital of Bosnia-Herzegovina - WRONG.
(B) Bosnia-Herzegovina is Sarajevo, whose population
- let's leave this alone, since there is doubt in the use of whose
(C) Bosnia-Herzegovina is Sarajevo, with a population
- The capital of Bosnia-Herzegovina is Sarajevo, with a population of was 51,919 - grammatical error - WRONG
(D) Bosnia-Herzegovina, Sarajevo having a population that
- The capital of Bosnia-Herzegovina, Sarajevo having a population that was 51,919 - verb tense error - WRONG
(E) Bosnia-Herzegovina, the population of Sarajevo
- The population of Sarajevo is NOT the capital of Bosnia-Herzegovina - WRONG.
The only remaining answer is B -
The capital of Bosnia-Herzegovina is Sarajevo, whose population was 51,919