The number of positive integral solutions of the equation x+y+z+t+e =

This is known as a "partition problem" in combinatorics. I've never seen a partition problem in any official GMAT material, so it's very unlikely anyone will need to understand how to solve this kind of problem. But if we take 10 dots:

• • • • • • • • • • 

then if we insert four 'partitions' between different pairs of dots, for example like this:

• | • • • | • •| • | • • • 

then we'll be finding a way to write "10" as a sum of five numbers. So in the example above, counting the dots in each zone from left to right, we're showing that 10 = 1 + 3 + 2 + 1 + 3. Any of the ways we can insert four partitions will give us a different way to arrive at "10" as a sum of five numbers, and since there are 9 spaces between dots, and we need to insert 4 partitions, the answer is 9C4 (since order does not matter - switching one partition symbol with another doesn't change how we're dividing the dots). So the answer is (9)(8)(7)(6)/4! = (9)(7)(2) = 126.