Is it possible for a company to show positive cash flows but be in grave trouble?

Yes. And there are many different ways this can occur. A common explanation for a company with a net loss to report a positive cash flow is depreciation expense. Depreciation expense reduces a company's net income, but it does not involve a payment of cash in the current period.

Another explanation involves accrual accounting. A corporation must report its expenses as they are incurred and that is often before the corporation pays the invoice. For example, a corporation with an accounting year ending December 31 might have a huge expense at the end of 2012, but the invoice is not due until January 2013. The 2012 net income was reduced, but the corporation's cash is not reduced until 2013. These are just two examples, but is very common for the cash flow to be positive.

This is a question that can easily stump a person, no matter how smart or prepared someone is for an interview. Which is why interviewers love to ask it. Do not get stuck or hung up on this question, no matter the experience level. Just answer the yes or no question and then another sentence to back up your answer, and move onto the next question.

Example:
It sure can. An example involves unsustainable improvements in working capital.

That's a very good question and one that came up in one of my classes and I remember it very well, because I was stumped on the answer at first. (Giving a long explanation as the one above is always a good tip to remember, because it buys the interviewee more time to think about their answer and it doesn't leave a lot of silence as you are preparing to answer the question.)