This is an example of where plugging in small values for x might be the fastest method.
Since this problem involves even and odd integers, we need to test both even and odd integers for x.

When x is EVEN:
Using x = 4 as the plug-in value, 2x = 8 and 3x = 12
Quantity A: 8 has 3 even factors (2, 4, and 8)
Quantity B: 12 has 2 odd factors (1 and 3)
Thus, Quantity A is greater when x is EVEN.

When x is ODD:
Using x = 5 as the plug-in value, 2x = 10 and 3x = 15
Quantity A: 10 has 2 even factors (2 and 10)
Quantity B: 15 has 4 odd factors (1, 3, 5 and 15)
Thus, Quantity B is greater when x is ODD.

Since the relationship between Quantity A and B differs depending on whether x is even or odd, the relationship cannot be determined from the info given.