Hi RiyaR,
What is the source of this question? I ask because there's a problem with some of the wording. I think that the "intent" of the question is that the tank will leak water UNTIL it's half empty, then it will stop leaking (otherwise on the last day, the remaining water won't actually be a "double" of the day before it). There's also the issue of "the leak" - are we meant to "remove" all the lost water at once or is the water escaping at a particular rate? GMAT questions are carefully worded to remove this type of "interpretational bias."
All that having been said, here's what I think the author of this question was "going for".....
We're told that a 10,200 gallon tank has a leak. With each passing day, twice as much water is lost as on the previous day. We're asked how many days does it take for the tank to be half empty (meaning 5100 gallons are lost).
Fact 1: 20 gallons lost on the first day.
From this, we could figure out how much is lost on each day (just keep doubling the number) and we would eventually hit the "half-way" point (5100 gallons lost) that we're asked about.
Fact 1 is SUFFICIENT
Fact 2: 2560 gallons lost on the last day.
From this, we can work backwards to figure out how much is lost on each prior day (dividing the number in half)
2560
1280
640
320
160
80
40
20
By adding up these numbers, we get exactly 5100 gallons, so we know how many days it takes to hit 5100 exactly. I believe that the author intends for this to be considered SUFFICIENT.
However, if we keep cutting the numbers "in half", we get...
10
5
2.5
Etc.
This would mean that it COULD take longer to hit the half-way point, but there wouldn't be an exact "end of day" when we hit the 5100 gallons (since we don't know if the water is automatically removed from the tank or if it's lost at a constant rate each day. In this scenario, Fact 2 would be INSUFFICIENT.
My guess is whoever wrote this considers the correct answer to be D, but this question has some real biases/problems, so you wouldn't see it on Test Day.
GMAT assassins aren't born, they're made,
Rich
