Ok, so I don't normally post here, but one of my private tutoring students pointed me to this thread.
So yeah, there are a lot of words in this problem, and it looks complicated. And if you actually start thinking about "E" and "S"
separately -- as most people on this thread seem to be doing -- then it becomes quite complicated indeed.
But ... we don't care about E, and we don't care about S. We care about E - S. That's a HUGE difference. (Analogy: I drive my car 54 miles. Do you know the starting odometer mileage? Nope. Do you know the ending odometer mileage? Nope. Do you know the difference between them? Yep, 54 miles.)
What affects E - S? To figure that out, temporarily forget that there are 30 numbers, and pretend there's just 1 number.
* If the number is rounded
up, then E - S is
positive. It's the amount by which the number is rounded up. (If you round 14.87 up to 15, then E - S is 0.13.)
* If the number is rounded
down, then E - S is
negative. It's the amount by which the number is rounded down. (If you round 14.77 down to 14, then E - S is -0.77.)
Thinking this way, we can see that it's a waste of time to consider the "integer part" at all. If you round 14.87 up to 15, or 99.87 up to 100, or anything point 87 up to the next integer, you're still looking at +0.13.
Now that we know that, things are more transparent.
* 10 numbers are rounded up.
The
most by which they can be rounded up is just barely less than 1 each (if you start with x.00001 type thing).
The
least by which they can be rounded up is just barely more than 0.1 each (if you start with x.89999 type thing).
* 20 numbers are rounded down.
The
most by which they can be rounded down is just barely less than 1 each (if you start with x.99999 type thing).
The
least by which they can be rounded down is 0.1 each (if you start with x.1).
To make E - S as big as possible, make the positive contributions as big as possible: 10 * (approximately +1) = approximately +10. Make the negative contributions as small as possible: 20 * -0.1 = -2. So, the maximum value of E - S is somewhere around 8.
To make E - S as small as possible, make the positive contributions as small as possible: 10 * (approximately 0.1) = approximately +1. Make the negative contributions as big as possible: 20 * (approximately 1) = approximately -20. So, the minimum value of E - S is somewhere around -19.
There you go.
The point here is that you should
think about whatever the problem actually asks you for. In those terms, it sounds stupidly simple, but look at what's happening in this thread -- everyone is thinking separately about E and S, even though we only care about E - S. (Think about the odometer.) Oops.
Focus!
This idea is even more important on data sufficiency problems. (If a data sufficiency problem asks for something minus something else, and you try to find the individual values of "something" and "something else" rather than just finding the difference, you're practically certain to get the problem wrong, even if your math is all correct.)
--
Ron Purewal
ManhattanGMAT
Un bon vêtement, c'est un passeport pour le bonheur.Yves Saint-Laurent
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Un bon vêtement, c'est un passeport pour le bonheur.
—Yves Saint-Laurent