Yeah, the cash flow can be tricky–especially in this fact pattern; as it appears as though one should use the direct method to solve. In solving this problem, you must understand how to account for the change in A/R. If you don't understand how changes in these activities impact underlying items (sales), then it will be really confusing.
To answer your questions in the order they appear:
1. “Secondly, after I saw the answer I was thinking that the $5,000 should be added for some reason.” Whenever A/R increases, you are reporting more income than you are collecting cash; on the cash flow, this is depicted as a (negative), or a USE of cash. So, instead of adding, you subtract this number.
2. “Also, I thought that the indirect approach always started at net income?” You are correct–in looking at the fact pattern, the author correctly started with net income of $60,000.
3. “Also, why did they say the used the indirect method to prepare the statements?” I believe this is just fodder. In solving the question, this statement is irrelevant because one can deduce that the indirect method is in use.
4. “Their solution implies that they are using the direct method to solve it?” Not so. The question is requiring you to “back into” the number of cash collected by netting the change in A/R with the revenue reported in 2010; the direct method is not in use here because the direct method would not incorporate the change in A/R.
5. “What if they had said they had used the direct approach to prepare the statements. Would the answer be the same?” No, the answer (nor the fact pattern) would be the same because, again, the direct method does not deal with changes in balance sheet accounts and other noncash items (depreciation).
In order to solve this problem, you take the $75,000 of revenue that was recognized (given) and subtract the increase in A/R. Why subtract? Because this is a use of cash; since the question is asking for cash receipts, the $5k change in A/R would be a reduction to cash receipts.
Let me know if you need more help.
Texas CPA - licensed in 2012!!!