Population Growth to Per Capital GDP

CFA Level II Economics
#1

“although population growth may increase the growth rate of the overall economy, it has no impact on the rate of increase in per capita GDP.”

The above statement is true only when the rate of growth of economy is proportional to the rate of population growth right?

If Economy growth rate is increasing at a higher rate than population growth rate then per capita GDP increases, right?

#2

You are right. In fact, the CFAI book shows a table (amazing btw) where you can see the per capita GDP growth of many countries. Japan for example showed an accumulated economy growth of 3000% (If I remember well) but the population just doubled or something like that.