My question is about the application of a technique which Ron taught- the shortcut approach to wt averages where you use the number line.I was able to apply that technique successfully to-Percents and Weighted Averages problem in the MGMAT FDP book-"Kris-P cereal is 10% sugar by weight, whereas healthier but less delicious
Bran-D cereal is 2% sugar by weight. To make a delicious and
healthy mixture that Is 4% sugar, what should be the ratio of Kris-P
cereal to Bran-D cereal, by weight?"

Can I also apply the same technique to Percent Change and Weighted Averages problems given in the MGMAT FDP book- question-A company sells only pens and pencils. The revenue from pen sales in 2007
was up 5% from 2006, but the revenue from pencil sales declined 13% over
the same period. If overall revenue was down 1% from 2006 to 2007, what
was the ratio of pencil revenues to pen revenues in 2oo6?.

If I can apply the same technique are there any tips-cause I couldn't solve this problem using the shortcut number line approach.

Yep, same approach is good. First, let’s go through this one algebraically: Old pens = x, new pens = 1.05x. Old pencils = y, new pencils = .87y. New revenue = 99% of old revenue so (1.05x + .87y) = .99(x + y).

1.05x + .87y = .99x + .99y
.06x = .12y
6x = 12y
x = 2y

We sold twice as many pens as pencils. Now let’s try the number line approach: Place the pens at +5 on the number line, the pencils at -13, and the balance point at -1. Remember the distance from the balance point to an endpoint gets multiplied by the weight of that endpoint, and this number should be the same on both sides. 6 (5 minus -1) times the number of pens = 12 (-1 minus -13) times the number of pencils. Again, we see that we sold twice as many pens as pencils. This technique doesn’t work with all conceivable situations though (look up the problem about the election and the two parties for a good example), so you need to consider this technique carefully. And if you aren’t 100% sure you can use the number line method, don’t use it..

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Tim Sanders
Manhattan GMAT Instructor