1. Notice that in each of the first 4 options the first word is WHICH. This relative pronoun is next to APPROACHES, and this proximity already means that it is much more likely to refer to APPROACHES than to VARIETY: therefore, the subsequent verb should be plural. Nevertheless, if you are in doubt, ask yourself about the logic of the situation: would it make any sense to say that VARIETY includes REDUCING EMPLOYMENT and USING NEW TECHNOLOGY? Clearly, it is the APPROACHES that do these things, not the VARIETY. You seem to have the idea that when you have a subject such as A VARIETY OF APPROACHES or A TROOP OF SOLDIERS or THE CATALOGUE OF PRODUCTS the verb must agree with the first noun in each phrase. Nevertheless, this is not necessarily the case.
Look at these examples:
The catalogue of products is lying on the table. (The CATALOGUE is lying, so the verb is singular.)
The catalogue of products that have been added to the inventory is lying on the table. (The relative clause
that have been added to the inventory modifies PRODUCTS and the verb is therefore plural; the second clause, on the other hand, has a singular verb, IS LYING, because its subject is CATALOGUE.
2. In option C of your example there is a grammatically-correct and logical relationship between APPROACHES, the relative pronoun, and the verb INCLUDE. There are also the two first parts of a three-part parallel structure: REDUCING ... USING ... AND FINDING. In option B, the verbs are also parallel, but the phrase
using new technology to be more efficient in pumping oil is verbose and unidiomatic, and leaves unclear who or what is going TO BE MORE EFFICIENT.
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