At the start of an experiment, a population consisted of x organisms.

Question

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 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

BrentGMATPrepNow · Answer

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

Aishwaryatyagi · Answer

Lets start with population and month:-

X-Start of first month(1)
2X-end(1)
2X-start(2)
4X-end(2)
4X-start(3)
8X-end(3)
8X-start(4)
16X-end(4)
16X-start(5)
32X-end(5)

now 32X>1000
=> value has to be 4(least value)
Hope this makes sense!

Gaurav2896 · Answer

I guess the answer is D ) 5 
Increase by 2 times means : x is increased by 2 times , so answer is 2x+x = 3x .(Increased to 2 times means 2x)
end of 1st month x -> 2x + x = 3x 
end of second month 3x -> 2(3x) +3x = 9x 
similarly , end of 5th month 243x.
Now 243x>1000 , so x >4 ,so minimum = 5.

stne · Answer

Month   \hspace{ 9mm}    Begining of month   \hspace{ 8mm}    End of Month   \hspace{ 9mm}     Total for the month

1 \hspace{ 30mm} x \hspace{ 36mm} 2x \hspace{ 39mm} 3x

2 \hspace{ 30mm} 3x \hspace{34mm} 6x \hspace{ 39mm} 9x

3 \hspace{ 30mm} 9x \hspace{34mm} 18x \hspace{ 35mm} 27x

4 \hspace{30mm} 27x \hspace{ 32mm} 54x \hspace{ 34mm} 81x

5 \hspace{ 30mm} 81x \hspace{31mm} 162x \hspace{ 32mm} 243x

We know  243x>1000

Hence  x > 5

Ans-D

Hope it's clear.

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

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At the start of an experiment, a population consisted of x organisms.

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At the start of an experiment, a population consisted of x organisms.

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