#) It is not just simply making one quantity greater than other and the other way around, make sure you do that while keeping these in mind. a) the values that you select should satisfy the given condition in the problem. b) when you plug those values in the given condition they should generate different set of outputs. (this applies to all types of problems)
#) To prove "D" is just one of the several strategies to solve QC problems. It really depends on the nature of a problem ; since you can use multiple approaches to derive the result. In several cases picking smart values might not be the ideal way to go.
#) I would not recommend hard wiring "method to pick smart numbers", yes you could definitely start with very easy values such as 0,100,1,10,0.5 (and narrow down your answer choices by the process of elimination). The only way to develop the intuition is to use those strategies and solve lots of problems and try to recognize patterns.
For general (Non-QC) questions, just solely picking smart numbers such as 100, should work fine. You probably wouldn't need to do anything "case test" as above!
For basic problems picking 100 is kind off safe. Further down the road you will come across a type called Variable in Choice where the above method of picking safe values such as "100" sometimes fails ; the case-test thing comes into play here ; but there are slightly modified strategies to deal with it.
case 1: No of students: 200, No of Faculty: 120 (Student > Faculty)
For Col A :
-> students who dine = 3/5 x 200 = 120
-> professors who dine = 1/6 x 120 = 20
Total : 140
Col B : total students + professors who do not dine = 80 + 100 = 180
Col B greater
Case 2: No of students: 50, No of Faculty: 180 (Student < Faculty)
-> students who dine = 3/5 x 50 = 30
-> professors who dine = 1/6 x 180 = 30
Col A : total students + professors who dine = 60
Col B : total students + professors who do not dine = 20 + 150 = 170
Again Col B greater
See the whole purpose of proving contradicting answer gets invalidated. And somethings this is the major flaw of picking values for QC ; given the time constraint it becomes difficult to capture the right set of values to prove "D".