The population in a certain town doubles every 5 years. Approximately

Question

The population in a certain town doubles every 5 years. Approximately how many years will it take for this town’s population to grow from 100 to 25000?

A. 15
B. 20
C. 30
D. 35
E. 40

Kudos for a correct  solution .

gmat6nplus1 · Answer

Now they are 100 in 5 years they will be 2(100). We want to figure out what power of 2 makes the total population greater than 250000.  2^8  is greater than 250k. thus 2 is compounded eight times. If every time that eight is compounded 5 years fly, then we need 40 years to overtake 250k.

Answer E.

PareshGmat · Answer

Answer = E. 40

Let "n" is the multiplication factor for 5 years

Equation setup would be as follows:

100 * 2^{\frac{n}{5}} = 25000

2^{\frac{n}{5}} = 250 \approx{256} \approx{2^8}

\frac{n}{5} = 8

n = 40

EMPOWERgmatRichC · Answer

Hi all,

In these types of questions, the answers are usually close enough "together" that accuracy is a MUST. If you're 'off', even a little bit, then you'll pick one of the wrong answers and not know it. As such, you should be prepared to do a bit of "brute force" work to make sure that your answer is correct.

Here, we're essentially asked to count "doubles" until we hit a certain level.

I'm going to remove two 0s from the 'start' and 'end' values to save on some note-taking. So, we start with 1 and we want to get to 250.....

Start = 1
1st double = 2
2nd = 4
3rd = 8
4th = 16
5th = 32
6th = 64
7th = 128
8th = 256

So it takes 8 "doubles" to get to the (approximate) goal. Since each "double" is 5 years of time, (8 doubles)(5 years each) = 40 years approx.

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

dharam831 · Answer

The population in a certain town doubles every 5 years. Approximately how many years will it take for this town’s population to grow from 100 to 25000?

A. 15
B. 20
C. 30
D. 35
E. 40

Initial population = 100
Ater 5 years = 200 (2*100)
After 10 years = 400 (2^2*100)
.
.
.
After 35 years = 2^7*100 = 12800
After 40 year = 2^8*100 = 25600

OA = E

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION

Correct answer: (E)

We can set up a chart to solve this question.

Time Population
0 100
5 200
10 400
15 800
20 1600
25 3200
30 6400
35 12800
40 25,600

So the answer is E, 40. Note that this problem can also be treated as an exponent question. If we want to know how many times something doubles, we’re essentially asked to find x in the expression 2^x. Here we can say 100∗2^x = 25000. 100∗2^x = 25000
2^x = 250.
2^8 = 256, so x is approximately 8. If the town doubles in size every 5 years, and it has to double 8 times to get to the desired population, then the answer is 5 * 8 = 40.

Vinayprajapati · Answer

x----------------2x--------------4x-----------------8x----------
2^0*x-----------2^1*1----------2^2*x-------------2^3*x----------
nth item 2^n*x = 25000
2^n =250
n=8 (2^8=256)

Each doubling takes five years so 5*8 =40

Hence E.

ritu1009 · Answer

Since population doubles therefore rate of increase is 100%.
25000=100(1+100/100)^n/5
25000=100(2)^n/5
250=(2)^n/5
2^8~(2)^n/5
8=n/5
n=40

Jawad001 · Answer

0 years 100
5 years 200
10 years 400
15 years 800
20 years 1600
25 years 3200
30 years 6400
35 years 12800
40 years 25600(E)

PolarisTestPrep · Answer

Hey guys,

Sometimes the intuitive clunky seeming solution saves you time:

100 * 2 = 200
*2 = 400
*2 = 800
*2 = 1600
*2 = 3200
*2 = 6400
*2 = 12800
*2 = 25600

It's not elegant, but it's effective. Shouldn't take more than 30 seconds

Now just count how many times it doubles there

It doubles 8 times

We are told that the population doubles every 5 years

8 * 5 = 40 years approximately

The answer is E

sharmashagun770 · Answer

I solved it using a different approach= Using GP Formula (Of course, not exactly)

r=2
S^n =25,000
a=100

25,000=100(2^n-1)/(2-1)

250= (2^n-1)
250+1=2^n
251=2^n

Now, approximately 256 (2^8) translates to 251. Now, n=8 but this represents the number of terms in the GP (=number of times the population has doubled) but we need the number of years till the given population is reached = 8*5=40 years.

Bunuel , can you please tell what I missed?

EMPOWERgmatRichC · Answer

Hi sharmashagun770, The prompt asks us APPROXIMATELY how many years it would take for the population to increase in the way described (including the fact that each "doubling" of the population takes 5 years). Your approach appears to have correctly done that, so what exactly do you think that you "missed?" GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com

The population in a certain town doubles every 5 years. Approximately

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The population in a certain town doubles every 5 years. Approximately

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