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Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
At the start of an experiment, a population consisted of x organisms.
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15 Aug 2021, 17:26
15 Aug 2021, 17:26
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At the start of an experiment, a 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 1,000, what is the minimum possible value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: At the start of an experiment, a population consisted of x organisms.
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11 Nov 2021, 12:40
11 Nov 2021, 12:40
motion2020 wrote:
At the start of an experiment, a 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 1,000, what is the minimum possible value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
NOTE: Don't make the same mistake I made and ignore the words "increased by" in the question.
So, each month, the population doesn't double; the population INCREASES by double the population from last month.
In other words, the population TRIPLES each month.
Let's start by using the table method to list the population for each month.
# months elapsed | population
0 | x
1 | (x)(3)
2 | (x)(3)(3)
3 | (x)(3)(3)(3)
4 | (x)(3)(3)(3)(3)
5 | (x)(3)(3)(3)(3)(3) = (3⁵)(x) = 243x
So 243x represents the population of organisms after 5 months.
We're told that which population is greater than 1,000.
So we can write: 243x > 1,000
Divide both sides of the inequality by 243 to get: x > 4.11
Since x must be an INTEGER, the minimum possible of x is 5
Answer: D
General Discussion
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: At the start of an experiment, a population consisted of x organisms.
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16 Aug 2021, 00:09
16 Aug 2021, 00:09
1
motion2020 wrote:
At the start of an experiment, a 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 1,000, what is the minimum possible value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
At start of month 1 = x
At end of month 1 = x + 2x = 3x
At end of month 2 = 3x + 6x = 9x
At end of month 3 = 9x + 18x = 27x
At end of month 4 = 27x + 54x = 81x
At end of month 5 = 81x + 162x = 243x > 1000
i.e. x > 4.11
Hence, option D
