How many test cases are necessary to cover all the possible sequences of paths for the following program fragment?

The answer to this question is 2 test cases. This is because two of the conditions are independent of each other. In order to make this easier for you to understand, you can put values for the conditions. Prepare to have another set of test values that are meant to go through the wrong path.

Take note that paths for 3 and 4 are both false which explains why the answer would be letter A. It is best to seek more information about it if you are not convinced or if you would need more details about how this is possible.