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Wanted to know how to target this type of questions:

Question: The value of certain thing increased from 150 to 800 in 4 years. What is the average percentage increase per year?

The average percentage increase denotes simple average growth. The answer will the total percentage increase divided by 4.

In this example, the percentage increase will be (550/150)*100 = 366.67%

And average % increase per year will be one fourth of that approx equal to 90%.

However, if the question has been what has been the compounded growth rate, then the best way to solve the question will be to go from answer choice.

As finding the fourth root as required in this example will not be possible without calculators.

Value increased from 150 to 800 in 4 yrs
So total increase is 650 in 4 yrs = 162.5 in each yr
inc in eash yr
1 yr= 162.5/150*100 aprrox>1
2 yr= 162.5/312.5*100 aprrox>1/2
3 yr= 162.5/475*100 aprrox>1/3
4 yr= 162.5/637.5*100 aprrox>1/4

Avg of this 4 gives the required avg

> (1+.5+.333+.25)/4
> 0.52
So more than 52 % increase on an Avg