Heyo Topspin,

GMATGuru's explanation here is Grade A. But just to make sure the science is clear here, this concept is applied whenever you have a weighted average question.

As a basic example:

The boys in a class weigh 50 pounds. The girls weigh 10 pounds. The average weight of a student in the class is 45 pounds.

The first thing you know is that there must be more boys than girls. Why? Because the class average is so much closer to the boys average than the girls average. That knowledge alone is enough to get you through a surprising number of weighted average questions.

But if you needed to know the exact ratio of boys to girls, you can use Guru's method:

If there were an equal number of boys and girls in the class, the girls are 35 pounds away from the class average, and the boys are 5 pounds away.

That's a ratio of 5:35, or 1:7. That means there are 7 times as many boys as girls. (The reason that Guru mentioned the reciprocal is that, whichever group is most distant from the mean actually has fewest members.)

Good luck!

-t