For this problem, we could also take an intuitive approach and avoid calculations.
We know that the water tank usually lasts 40 days, but with a leak of 10 litres/day it will last only 30 days.
That means that 30 days of leaking loses 10 days worth of water for the village. Now if the leak is doubled to 20 litres/day, 30 days of leaking would lose 20 days of water for the village. But the supply would now last
less than 30 days (since the tank is losing more water each day). So the amount of water lost must be
less than 20 days worth.
Therefore, the amount of water lost must be
between 10 and 20 days worth, so the water tank will last the village somewhere between 20 and 30 days.
Looking at the answer choices, only one option is between 20 and 30 days. Answer D, 24 days.
Note that this approach only works because there is only one answer choice between 20 and 30. If the answer choices included multiple answers between 20 and 30 (e.g. 22, 24, 25), then you would need to do the calculations to determine the correct answer.
It is important on the GMAT to have a good intuitive feel for problems. It doesn't mean you'll be able to find every answer without doing any calculations, but it can help to narrow down answer choices if you know the answer must be in a certain range or of a magnitude. It is always good to think about the problems beyond the numbers to get a good understanding of what is going on.
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Dave de Koos
GMAT aficionado