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A tells us that the government had faced insolvency. B contradicts it by saying that the Minister's family had lived well despite the insolvency. BUT and WHILE can be used to indicate this contradiction and join the statements. C tells us the cause for why the Minister's family had lived well. SINCE and AS can be used as connectors here. The possible combinations are 2 and 1, 2 and 4, 3 and 1 & 3 and 4, out of which only the third is given in the options. The joined sentence will be: "Much of the government, including the public hospital system, faced insolvency while the Minister's family had lived large since they owned 38 properties in Guatemala and neighboring countries." Thus, (c) is the right answer.
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