I came across the PS problem below in the Kaplan quant workbook and do not feel that the recommended solution is necessarily the most comprehensive approach (for me at least). I'd love to see examples of how others might work this out.
Kaplan Math Workbook
6th Addition
Problem 22, Page 63
The population of a certain town increases by 50% every 50 years. If the population in 1950 was 810, in what year was the population 160?
a) 1650
b) 1700
c) 1750
d) 1800
e) 1850
Answer: c) 1750
Kaplan's solution:
"Since the population increases by 50% every 50 years, the population in 1950 was 150%% or 3/2 of the 1900 population. This means the 1900 population was 2/3 of the 1950 population. Similarly, the 1850 population was 2/3 of the 1900 population, and so on. We can just keep multiplying by 2/3 until we get to a population of 160."
1950: 810 x 2/3 = 540 in 1900
1900: 540 x 2/3 = 360 in 1850
1850: 360 x 2/3 = 240 in 1800
1800: 240 x 2/3 = 160 in 1750
Kaplan Math Workbook
6th Addition
Problem 22, Page 63
The population of a certain town increases by 50% every 50 years. If the population in 1950 was 810, in what year was the population 160?
a) 1650
b) 1700
c) 1750
d) 1800
e) 1850
Answer: c) 1750
Kaplan's solution:
"Since the population increases by 50% every 50 years, the population in 1950 was 150%% or 3/2 of the 1900 population. This means the 1900 population was 2/3 of the 1950 population. Similarly, the 1850 population was 2/3 of the 1900 population, and so on. We can just keep multiplying by 2/3 until we get to a population of 160."
1950: 810 x 2/3 = 540 in 1900
1900: 540 x 2/3 = 360 in 1850
1850: 360 x 2/3 = 240 in 1800
1800: 240 x 2/3 = 160 in 1750
