Gracespa

曼哈顿论坛上的解释
if you open a sentence with "like X, ..." then the following two things must be true:
1 * X is a noun (or something else that can function as a noun, such as a gerund, noun-type phrase, etc). in other words, X should not be a clause
2 * you INTEND a COMPARISON between X and the SUBJECT of the following sentence.

if these 2 things are not true, you can't use "like".

in choice (e), the second of these is not true, because the SUBJECT is not "hungary". the subject is "an overwhelming proportion of women". that's not a sensible comparison.
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in particular, you can't use "like" with prepositional phrases. in that case, you have to use "as", as in the correct answer.
(hey, i did it in that sentence, too. and not even on purpose. sweeeeeeet)