How to find the number of test cases needed when given a set of conditions?

I'm taking the ISTQB Foundation Level Certification Exam this Friday and while going over the sample exam on the ASTQB website I stumbled upon this question:
"You have been given the following conditions and results from those condition combinations. You can only have one form of payment. A PIN is only needed for a debit card. Given this information, using the decision table technique, what is the minimum number of test cases you would need to test these conditions?"
Conditions:
Valid cash Valid credit card Valid debit card Valid PIN Bank accepts Valid Selection Item in Stock
Results:
Reject Cash Reject Card Error Message Return Cash Refund Card Sell Item
Answers:
a. 7 b. 13 c. 15 d. 18
The answer is C. 15, but their explanation is simply a large decision table with all the combinations. This is great and all, but I don't have time to create a big, relatively complicated decision table with all 15 combinations/columnsI will only have 60 minutes to complete the 40 question test.
Is there an easier/simpler way to find how many combinations/columns/test cases would be needed to test these conditions?
Thanks!

I don't know on which ISTQB site you found the example but I found a PDF with examples here (see #24). In contrast to the exercise you posted, the example above mention the usage of a method called decision table technique.
You should solve it using decision tables because
 you are in the context of ISTQB and and should be prepare yourself for the test and (more important) for your professional life.
 unlike the way of doing it as suggested by Tam Minh you have a more formal way of "solving" those problems with the decision table technique.
Particularly, the second point is important when you have to explain yourself on what your resulting test cases are based on.