Sentence Correction

Freedman's survey showed that people living in small towns and rural areas consider themselves no happier than do people living in big cities.
(A) no happier than do people living
(B) not any happier than do people living
(C) not any happier than do people who live
(D) no happier than are people who are living
(E) not as happy as are people who live


According to me the correct answer is A.
Options D and E: They get cancelled out as they are not at all parallel as they both use the word
'who' for the modifying the people living in big cities.

Options B and C: Both the options get cancelled out as 'not any happier' is not idiomatic in GMAT as well as in Degrees of comparison..

Hence we are left with A
A is parallel as well as clarifies the meaning....

Is my explanation right, please give explanations for all the options.....