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Town A has a population of 160,000 and is growing at a rate
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30 Jul 2018, 10:31
30 Jul 2018, 10:31
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Question Stats:
74% (01:44) correct
25% (01:47) wrong based on 284 sessions
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Town A has a population of 160,000 and is growing at a rate of 20% annually. Town B has a population of 80,000 and is growing at a rate of 50% annually.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The number of years until town B’s population is greater than that of town A |
3 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: Town A has a population of 160,000 and is growing at a rate
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04 Aug 2018, 06:02
04 Aug 2018, 06:02
4
sandy wrote:
Town A has a population of 160,000 and is growing at a rate of 20% annually. Town B has a population of 80,000 and is growing at a rate of 50% annually.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The number of years until town B’s population is greater than that of town A |
3 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Let's keep track of each population for 3 years
TOWN A
Present Population: 160 (we'll drop the 000's at the end for both populations)
Population in 1 year: (160)(1.2)
Population in 2 years: (160)(1.2)(1.2)
Population in 3 years: (160)(1.2)(1.2)(1.2) = (160)(1.2)³
TOWN B
Present Population: 80
Population in 1 year: (80)(1.5)
Population in 2 years: (80)(1.5)(1.5)
Population in 3 years: (80)(1.5)(1.5)(1.5) = (80)(1.5)³
Now that we know the populations after 3 years, we can check whether or not 3 years is enough time for Town B's population to exceed Town A's population.
So, let's examine the fraction: (160)(1.2)³/(80)(1.5)³
There are 3 possible cases:
case a) (160)(1.2)³/(80)(1.5)³ = 1, in which case, the 2 populations are EQUAL
case b) (160)(1.2)³/(80)(1.5)³ < 1, in which case, Town A's population is LESS THAN Town B's population
case c) (160)(1.2)³/(80)(1.5)³ > 1, in which case, Town A's population is GREATER THAN Town B's population
160/80 = 2 and (1.2)³/(1.5)³ = (1.2/1.5)³ = (12/15)³ = (4/5)³ = 64/125
So, (160)(1.2)³/(80)(1.5)³ = (2)(64/125) = 128/125
Since 128/125 > 1, we have a case c situation.
So, after 3 years, Town A's population is still GREATER THAN Town B's population
So, it will take MORE THAN 3 YEARS for Town B's population to exceed Town A's population
We get:
Quantity A: MORE THAN 3 YEARS
Quantity B: 3 years
Answer: A
Cheers,
Brent
Re: Town A has a population of 160,000 and is growing at a rate
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06 Aug 2018, 00:26
06 Aug 2018, 00:26
1
I solved this question on paper, and it took me 05 minutes 20 seconds to get the answer. I went through the traditional percentile method year by year. The answer was right, but I am worried about taking a long time to solve it.
