The population of City X doubles every 25 years

BTGmoderatorLU wrote:The population of City X doubles every 25 years. If this rate continues for the foreseeable future, how many centuries will it take for the population to increase from 20,000 to 1,280,000?

A. 6
B. 4.5
C. 2.5
D. 2
E. 1.5

Let's make a table

TIME | POPULATION
Now: 20,000
25 years from now: 40,000
50 years from now: 80,000
75 years from now: 160,000
100 years from now: 320,000
125 years from now: 640,000
150 years from now: 1,280,000

So, it will take 150 years (aka 1.5 centuries) for the population to reach 1,280,000.

Answer: E

Cheers,
Brent

Hi All,

We're told that the population of City X doubles every 25 years and that this rate continues for the foreseeable future. We're asked for the number of CENTURIES (re: 100 years periods) it will take for the population to increase from 20,000 to 1,280,000. Since the question does NOT use the word 'approximate', we now that there is an EXACT answer. You might find it easier to determine that answer if you remove the 0s from the two given values:

If we're going from 2 to 128 by repeatedly 'doubling', then you might recognize that 'powers of 2' involved here:
2, 4, 8, 16, 32, 64, 128

That's 6 'doubles' from 2 to 128, so it took (6)(25) = 150 years = 1.5 centuries

Final Answer: E

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

BTGmoderatorLU wrote:The population of City X doubles every 25 years. If this rate continues for the foreseeable future, how many centuries will it take for the population to increase from 20,000 to 1,280,000?

A. 6
B. 4.5
C. 2.5
D. 2
E. 1.5

We are given that the population of City X doubles every 25 years. We need to determine the number of centuries it will take the population to increase from 20,000 to 1,280,000.

We can start by making a list (or table) that keeps track of doubling the population every 25 years:

Current: 20,000
After 25 years: 40,000
After 50 years: 80,000
After 75 years: 160,000
After 100 years: 320,000
After 125 years: 640,000
After 150 years: 1,280,000

Thus, it takes 150 years, or 1.5 centuries, to increase the population from 20,000 to 1,280,000.

Answer: E