1. In respect of what you say about option E, LIKE is in fact incorrectly used. It is not possible to compare a noun or a noun phrase (MUCH OF EASTERN EUROPE) with a prepositional phrase (IN HUNGARY). LIKE compares nouns, pronouns, and noun phrases. (Furthermore, option E attempts to connect two independent clauses with a comma:
an overwhelming proportion of women work, many are in middle management and light industry. This error is called a comma splice and always indicates a wrong answer in Sentence Correction.)
2. You say that the correct answer, option C, has no verb, but if you rearrange the sentence a little, you will see it.
In Hungary ... an overwhelming proportion of women work. And the sentence is telling us that this is also the case in much of Eastern Europe. In other words,
In much of Eastern Europe ... an overwhelming proportion of women work. Thus, WOMEN WORK in both places. The function of AS here is not exactly to compare but rather to say that what applies in Hungary applies in most of Eastern Europe: AS indicates that IN both places the situation is THE SAME.
Look at these examples, in which AS indicates the sameness of the situations:
On beaches, as in forests, there is abundant and varied wildlife.
In novels, as in plays, characters are presented and dramatic situations evolve.
For Hindus, as for Sikhs, Jains, and some Buddhists,
Diwali is a time of festivity and celebration.
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