1. Since the underlined part of the given sentence begins with THAN, it starts well: LOWER THAN. So therefore does option B.

2. LOWER AS COMPARED WITH in options C, D, and E is not possible: a comparison of inequality can use only THAN. (HIGHER THAN, MORE OFTEN THAN, BETTER THAN, and so on.) Eliminate these three.

3. In option A, the rest of the comparison is impossible. The sentence states that the average number ... was lower than what the hotel industry average did. Everything is bad here. First, we do not know what the hotel industry average DID: the sentence does not tell us, and is therefore comparing an average number with an enigma. Second, an average cannot DO anything: this idea is nonsensical. Third, the comparison is an ungrammatical mess, because it is made between a NUMBER and WHAT THE HOTEL INDUSTRY AVERAGE DID - in other words, between a noun and a clause.

There is also a defective comparison at the end of option A: occupancy and room rates grew faster than the average hotel. Do hotels grow? And if they do (a notion difficult to sustain), what does it mean to say that they grew more slowly than occupancy and room rates? How would one compare the rate of growth of an hotel (assuming that it could indeed grow) with the rate of growth of those two factors? The comparison makes no sense at all.

4. Only option B remains. The comparison is good: the average number ... was lower than the hotel industry average. In other words, an average number is compared with an average. This makes sense.

In respect of your question about THIS and THESE: in option B, THIS is a demonstrative adjective modifying PERIOD, and THESE is a demonstrative adjective modifying CHAINS.

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