Question Bank Fractions #4

[Guest]

On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 of that same year, 2/7 of the x liters have evaporated. This pattern continues such that by the end of each subsequent year the lake has lost 2/7 of the water that it contained at the beginning of that year. During which year will the water in the lake be reduced to less than 1/4 of the original x liters?


a) 2077
b) 2078
c) 2079
d) 2080
e) 2081

My approach to this problem was to use VIC, but I would have never thought of picking 4 like the answer suggested. Can anyone please let me know how you would approach this kind of problem, particularly how to pick smart numbers?

Thanks.

[dbernst]

Guest, this is a very good question. I too did not originally consider 4 as a selection; instead I chose a multiple of 7 and 4 - the 7 to at least easily calculate the first reduction in 2076, and the 4 to have a whole number for 1/4 of the total number of liters.

My number (28) was definitely a bit unwieldy, but the problem was still solvable in 2 minutes.

Though choosing a "good" number is difficult in this problem, the general rule is to choose numbers that are easily divisible by values in the problem (eg. if the problem asks for 1/3 of the total and then another 1/4, choose 12), easily converted to different units (eg. if the problem gives you seconds but asks for minutes, choose a multiple of 30), or just easy to manipulate (eg. if the problem concerns percents, choose 100).

I hope that helps.
-dan

[Katie]

What kind of equation would you use for this problem?

[StaceyKoprince]

Personally, I would never use an equation for this GMAT problem - it would be much too complex to set up and solve without a calculator in 2 minutes. But you can write an equation based on the standard compound interest formula.

Here it is (but don't actually use it!):

Future Value = Present Value * (1+rate)^period
so our PV = x, rate = -2/7 (it's declining, remember), and period = t:
x(1-2/7)^t < (1/4)x
You have to solve for t, which is an exponent. That's why you really don't want to solve this algebraically.

[SHAFTBMF]

I did not see an answer provided to this question regarding the math bank fraction question. please post

[StaceyKoprince]

Oops, sorry! Answer is D.