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

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Math Expert
Joined: 02 Sep 2009
Posts: 55228
At the start of an experiment, a certain population consisted of x org  [#permalink]

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27 Sep 2018, 05:38
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35% (medium)

Question Stats:

47% (01:39) correct 53% (01:50) wrong based on 16 sessions

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At the start of an experiment, a certain population consisted of x organisms. At the end of each month after the start of the experiment, the population size increased by twice of its size at the beginning of that month. If the total population at the end of five months is greater than 1000, what is the minimum possible value of x?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

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

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27 Sep 2018, 06:52
Bunuel wrote:
At the start of an experiment, a certain population consisted of x organisms. At the end of each month after the start of the experiment, the population size increased by twice of its size at the beginning of that month. If the total population at the end of five months is greater than 1000, what is the minimum possible value of x?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Initial size = x
Increase = 2x
Final size after first increase = $$3x$$

After 5 months Population = $$3^5*x$$

Now, $$3^5*x > 1000$$

i.e. 243x > 1000
i.e. x > 4.1

i.e. $$x_{min} = 5$$

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

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27 Sep 2018, 07:22
Bunuel wrote:
At the start of an experiment, a certain population consisted of x organisms. At the end of each month after the start of the experiment, the population size increased by twice of its size at the beginning of that month. If the total population at the end of five months is greater than 1000, what is the minimum possible value of x?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

At the time of Start is x
Size after 1st Month is 3x (ie x + 2x)
Size after 2nd Month is 9x (ie 3x + 2*3x)
Size after 3rd Month is 27x (ie 9x + 2*9x)
Size after 4th Month is 81x (ie 27x + 2*27x)
Size after 5th Month is 243x (ie 81x + 2*81x)

Quote:
Given: If the total population at the end of five months is greater than 1000

Or, $$243x > 1000$$

So, $$x > 4.11$$, Thus among the given optionthe s, answer must be (D) 5
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Re: At the start of an experiment, a certain population consisted of x org   [#permalink] 27 Sep 2018, 07:22
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