please see the below question and the explanation... In the question the city population increase by 10% per year. How then the population can be exactly double the population of one year ago? I do not get it
QUESTION from Manhattan test:
Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year?
20%
40%
50%
65%
75%
Explanation:
This problem can be solved most easily with the help of smart numbers. With problems involving percentages, 100 is typically the ‘smartest’ of the smart numbers.
If we assume that today’s population is 100, next year it would be 1.1 × 100 = 110, and the following year it would be 1.1 × 110 = 121. If this is double the population of one year ago, the population at that time must have been 0.5 × 121 = 60.5. Because the problem seeks the “closest” answer choice, we can round 60.5 to 60.
In this scenario, the population has increased from 60 to 100 over the last year, a net increase of 40 residents. To determine the percentage increase over the last year, divide the net increase by the initial population: 40/60 = 4/6 = 2/3, or roughly 67%.
For those who prefer the algebraic approach: let the current population equal p. Next year the population will equal 1.1p, and the following year it will equal 1.1 × 1.1p = 1.21p. Because the question asks for the closest answer choice, we can simplify our algebra by rounding 1.21p to 1.2p. Half of 1.2p equals 0.6p. The population increase would be equal to 0.4p/0.6p = 0.4/0.6 = 2/3, or roughly 67%.
The correct answer is D.
You must select an answer to proceed.
Well, I think its clearly mentioned in th question that the population will increase at a rate of 10% over the next two years only & no where in the question is mentioned that at the same rate the population was increased over the last year. Actually you caught in trap set by the question.