Day 24 - Finished Kaplan Arithmetic Chapter
This afternoon I finished the rest of the Arithmetic chapter in the Kaplan Math Workbook, pages 36-71. Like I said before, it's a slow read but very comprehensive.
One lesson that I really enjoyed in this chapter was Kaplan's strategies for thinking about averages (arithmetic means). Kaplan advocates thinking about averages as balanced values--as an example, say you have the following problem:
The average of 3, 4, 5, and x is 5. What is the value of x?
Instead of delving into time-consuming algebra to solve this problem (maybe not so time consuming with this specific problem), think about how each number is positioned relative to the average of five:
3 is 2 less than 5. (-2)
4 is 1 less than 5. (-1)
5 is the average. (0)
x must be 3 more than the average to balance the set of numbers at a mean of 5. This counterbalances the -3 value created by the set of numbers given in the problem.
Thus, x = 8.
Perhaps this balancing idea is intuitive to a lot of readers out there all ready, but I've never thought of averages in this fashion. Doing so has allowed me to speed through these types of problems dramatically. Heck yes.
SUMMARY OF DAY 24 WORK:
1. Finished Chapter 2 - Arithmetic in Kaplan Math Workbook, pages 36-71.
RECAP OF DAY 24 INSIGHTS:
1. Kaplan's strategy for dealing with averages is cool.
Labels: GMAT Math