by **StaceyKoprince** Thu Feb 28, 2008 10:26 pm

Estimation is not too bad for the first couple. If it has x liters at the beginning of 76 and 2/7 evaporates at the 2nd of 76, that's still more than half left. If another 2/7 (of what's left) evaporates by end of 77, that's till not going to be enough to get me down to 1/4 of my original. If you think about it, you can generally see that the first couple of years won't be enough time (because, each time, a smaller volume is evaporating, since it's always only 2/7 of what's left).

I'll tell you something that should you relieve your mind about the test (if not our materials): the test wouldn't give you the question in quite this way. Either the numbers would be easier to work with and the answer choices would be close together OR the numbers would be hard just like this but the answer choices would be further apart.

Let's assume we had the latter scenario: what I'd really want to do here is pick an answer choice and work backwards.

If C 2079 is the answer, and every year I have 5/7 left at the end of the year (compared to what I started with) 5/7 is approximately 70%. So I lose 30% over the year and have 70% left, each year. Let's say I have 7 (gallons?) at year end (YE) 79. Then I finished 78 / started 79 with 10 gallons. If YE78 was 10 gallons (or 70%), then I finished 77 / started 78 with about 14 gallons (just estimate here). If YE77 was 14 gallons (or 70%), then I finished 76 / started 77 with about 20 gallons. If YE76 was 20 gallons, then I finished 75 / started 76 with about 28 gallons.

(how am I doing that math by the way? Each time, divide by 7 - very roughly - then add that number three times to your starting point. eg, for 10: 10/7 is about 1.3 or 1.4. 10 + 1.3 + 1.3 + 1.3 is about 14. etc.)

So I started with 28 and ended with 7, which is about 1/4. Now, in this case, that's not close enough to tell us the answer definitively (technically, we want LESS THAN 1/4 so this isn't quite enough time - except I was estimating...)

But on the real test, when your years would be further apart with this kind of math, this would be close enough to tell.

Stacey Koprince

Instructor

Content & Curriculum Lead

ManhattanPrep