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Math Expert V
Joined: 02 Sep 2009
Posts: 65785
At the start of an experiment, a certain population consisted of 3  [#permalink]

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32 00:00

Difficulty:   5% (low)

Question Stats: 90% (01:26) correct 10% (01:51) wrong based on 1584 sessions

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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)

Kudos for a correct solution.

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At the start of an experiment, a certain population consisted of 3  [#permalink]

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7
3
At time when the experiment started , Population N = 3
At end of the first month , Population N1= 3x2 = 6
At end of the second month , Population N2= 6x2 = 12 =$$3 * 2^{2}$$

At the end of nth month , Population Nn = $$3 * 2^{n}$$

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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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1
3*2^n where n is the #of month --> 3*2^10 Answer (D)
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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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1
Bunuel 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)

Kudos for a correct solution.

My Solution:

At the end of every month the population size doubles, so,

After 10 months the population becomes 3072 (3,6,12,24,48,96,192,384,768,1536,3072)

Then find the prime factors of 3072 i.e 3 (2^10) Option D

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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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5
At the beginning of the month the number is 3;
At the end of 1st month number is 3*2
At the end of 2nd month number is 3*2^2
hence at the end of 10th month =3*2^10
Senior Manager  D
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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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1
population at starting of experiment = 3
at the end of 1st month population = 3 * 2
at the end of 10th month population = 3 * 2^10

Manager  B
Joined: 12 Feb 2011
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At the start of an experiment, a certain population consisted of 3  [#permalink]

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1
Common ratio of increase = 2 and doubling started from end of first month, therefore nth term will be provided by $$initialvalue*r^n$$, i.e. in this case 3*2^10.
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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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1
A very simple formula that always helps me with these types of questions:

Final population = S * P ^ (t/i)
S -> starting population
P -> progression (2 - doubles, 3- triples etc.)
t -> time
i -> interval

In our case it is a simple solution, which is : Final population = 3 * 2 ^ (10/1)
so it is 3 * 2^10 -> D
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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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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....

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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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BPHASDEU wrote:
A very simple formula that always helps me with these types of questions:

Final population = S * P ^ (t/i)
S -> starting population
P -> progression (2 - doubles, 3- triples etc.)
t -> time
i -> interval

In our case it is a simple solution, which is : Final population = 3 * 2 ^ (10/1)
so it is 3 * 2^10 -> D

$$Final\quad Population\quad =\quad { S\ast P }^{ \left( \frac { t }{ i } \right) }$$

Very useful - I did not recognize the pattern and ended up doubling the values until the 10th month. Then I prime factorized 3072 and when I saw 1024, I knew there was an easier way to solve it (Actually, I had known it from the very beginning but just couldn't figure it out).
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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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3
Bunuel 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)

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:

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

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Director  G
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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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2
I think its a GP:
3*2, 3*2*2, 3*2*2,.....................

First term= 6
Common ratio= 2

10th term= first term*common ratio^(n-1)
= 6*2^9
=2*3*2^9
=3*2^10
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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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each month doubled means for each month multiply by 2
so 3*(2*2*2*10times)
3*(2^10)
Intern  B
Joined: 05 Feb 2017
Posts: 34
Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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End of 1st Month population =3*2

End of 2nd Month population =3*2*2

Therefore at the end of 10 th Month it will be
3*(2^10)

Hence D

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Re: At the start of an experiment, a certain population consisted of 3  [#permalink]

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_________________ Re: At the start of an experiment, a certain population consisted of 3   [#permalink] 31 Aug 2019, 06:30

# At the start of an experiment, a certain population consisted of 3  