Problem Solving

Hi talaangoshtari,

This question is perfect for TESTing THE ANSWERS (as David and Mitch have shown). The concept behind the prompt is similar to an interest-rate question though, so you can set it up that way (and do a bit of estimation to get to the correct answer).

We're given a couple of facts to work with:
1) The population increases 50% every 50 years
2) The population in 1950 was 810

We're asked to find the YEAR in which the population was 160.

Using the Compound Interest Formula, we'd have....

Principal = 160
Interest rate = 50% = .5
Time = (Blocks of 50 years)

160(1.5)^T = 810

While trying to solve for the exact value of T could be a bit tedious, we can use estimation...

(1.5)^T = 810/160
(1.5)^T = about 5

1.5^1 = 1
1.5^2 = 2.25
1.5^3 = about 3.33
1.5^4 = about 5

So, 4 "blocks" of 50 years would have to have passed for the population to go from 160 to 810

1750 +50+50+50+50 = 1950

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

When you increase something by 50%, you multiply it by 1.5, or 3/2. So in this question, when we go forward 50 years, the population is multiplied by 3/2. So if instead we want to go back in time 50 years, we'd multiply by 2/3. To go from 810 to 160, we need to multiply by 160/810 = 16/81 = (4/9)^2 = (2/3)^4 so we need to multiply by 2/3 four times, which corresponds to going back in time 4*50 = 200 years. So the answer is 1750.

talaangoshtari wrote:The population of a certain town increases by 50 percent 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

We can create the following equation:

160(1.5)^n = 810

(3/2)^n = 810/160

(3/2)^n = 81/16

Since 3^4 = 81 and 2^4 = 16, we see that n must be 4 so that (3/2)^n = 81/16. However, here n represents the number of 50-year periods that it took for the population to increase from 160 to 810. Thus, the number of years was 4(50) = 200 for the population of 160 to reach a population of 810 in 1950. So, the population of 160 must have occurred in 1750.

Answer: C