At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 10 months?
A) 2^3
B) 3^2
C) 2(3^10)
D) 3(2^10)
E) 3(10^2)
OA: D
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At the start of an experiment,
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boomgoesthegmat
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This is a great candidate for creating a growth table (for more on this see this video: https://www.gmatprepnow.com/module/gmat ... /video/929 )boomgoesthegmat wrote:At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 10 months?
A) 2^3
B) 3^2
C) 2(3^10)
D) 3(2^10)
E) 3(10^2)
- Start: 3 animals
- End of month 1: (3)(2) animals [since the population doubles each month]
- End of month 2: (3)(2)(2) animals
- End of month 3: (3)(2)(2)(2) animals
- End of month 4: (3)(2)(2)(2)(2) animals
.
.
.
We can see the pattern and recognize that, at the end of month 10, we'll have the product of one 3 and ten 2's.
.
.
- End of month 10: (3)(2)^10
Answer: D
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Population at start = 3boomgoesthegmat wrote:At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 10 months?
A) 2^3
B) 3^2
C) 2(3^10)
D) 3(2^10)
E) 3(10^2)
OA: D
Population at end of 1st month = 2*3
Population at end of 2nd month = 2^2*3
....
....
Population at end of 10th month = 2^10*3
Correct Option: D
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We are given that a certain population consisted of 3 animals and that at the end of each month after the start of the experiment, the population size was double what it had been at the beginning of that month. Thus:boomgoesthegmat wrote:At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 10 months?
A) 2^3
B) 3^2
C) 2(3^10)
D) 3(2^10)
E) 3(10^2)
End of Month 1 = 3 x 2 = 3 x 2^1
End of Month 2 = 3 x 2 x 2 = 3 x 2^2
End of Month 3 = 3 x 2 x 2 x 2 = 3 x 2^3
We see that after each month the value increases by a factor of two. Thus:
End of Month 10 = 3 x 2^10
Answer: D
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Hi All,
This is a great 'concept' question - if you recognize the concept involved, then you don't have to do any actual math to solve this problem. If you're not sure how the math 'works' however, you can still use a bit of 'brute force' to define the pattern involved and still get the correct answer.
We're told that a population starts with 3 animals and at the end of each month, the population DOUBLES. We're asked for the size of the population at the end of 10 months.
Based on the 'growth' that's defined, we can list out the first few months worth of data for reference....
Start = 3 animals
Mo. 1 = 3(2) = 6 animals
Mo. 2 = 6(2) = 12 animals
Mo. 3 = 12(2) = 24 animals
Etc.
Notice how each month we multiply the prior month by TWO. That is the pattern involved. We start with 3, then multiply by 2 over-and-over. Since there are 10 months, there will be 10 "multiply by 2s", so the correct answer must be....
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This is a great 'concept' question - if you recognize the concept involved, then you don't have to do any actual math to solve this problem. If you're not sure how the math 'works' however, you can still use a bit of 'brute force' to define the pattern involved and still get the correct answer.
We're told that a population starts with 3 animals and at the end of each month, the population DOUBLES. We're asked for the size of the population at the end of 10 months.
Based on the 'growth' that's defined, we can list out the first few months worth of data for reference....
Start = 3 animals
Mo. 1 = 3(2) = 6 animals
Mo. 2 = 6(2) = 12 animals
Mo. 3 = 12(2) = 24 animals
Etc.
Notice how each month we multiply the prior month by TWO. That is the pattern involved. We start with 3, then multiply by 2 over-and-over. Since there are 10 months, there will be 10 "multiply by 2s", so the correct answer must be....
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
