When work is not started at the same time, it can be confusing to work with rate formulas and figure out the exact equations for someone that is not used to this on a daily basis (99% of GMAT applicants?). So it is useful to pick numbers and/or try the answers.
If A can fill the tank in 6 hours and B can empty it in 4 hours, let's choose a capacity of 12 liters for the tank (least common multiple) to make the math as easy as possible.
This means that A pumps 2 liters / hour to fill it in 6 hours, and B takes out 3 liters / hour to empty it in 4 hours.
It is now clear that, working together, 1 liter / hour is removed from the tank.
Now let's take a look at the answers. Strategy says that we should start with answer B or D, because we have a higher chance of getting it right in the first shot (see note below). But we can also pick the easiest number to work with and see what happens, so let's take 2 (we could take 1 but I'll go to the answer in the middle. Starting by trying A or E is the worst option).
After 2 hours, the tank has 4 liters. A and B together would need 4 more hours to empty it. That is a total of 6 hours, but we want a total of 7h30 (9 am to 4:30 pm).
Let's try answer D, 2.5 hours. After this time, the tank has 5 liters. Together A and B will need 5 more hours to empty it. This makes it a total of 7.5 hours.
Answer D.
Note:
1) Let's say you choose to try B. If it's not the correct solution but you know it must be a lower value, the answer will be A.
2) Let's say you choose to try D. If it's not the correct solution but you know it must be a higher value, the answer will be E.
This is better than choosing C: if you know it's a lower value you still have to try A or B. If you know it's a higher value, you still have to try D or E.
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