GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 19 Jan 2020, 20:16

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The population of a certain town increases by 50 percent every 50 year

Author Message
TAGS:

### Hide Tags

BSchool Moderator
Joined: 19 Feb 2010
Posts: 294
The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

20 Sep 2010, 10:10
8
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:12) correct 32% (02:19) wrong based on 233 sessions

### HideShow timer Statistics

The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?

A. 1650
B. 1700
C. 1750
D. 1800
E. 1850
Math Expert
Joined: 02 Sep 2009
Posts: 60496
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

20 Sep 2010, 10:20
4
6
cano wrote:
The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?

A. 1650
B. 1700
C. 1750
D. 1800
E. 1850

Increase by 50% = times 1.5, so if the population at a certain year were 10 then in 50 years it would be 10*1.5 and in 50*2=100 years it would be 10*1.5*1.5=10*1.5^2 --> $$160*1.5^n=810$$, where $$n$$ is the # of 50-year periods --> $$(\frac{3}{2})^n=\frac{81}{16}=(\frac{3}{2})^4$$ --> $$n=4$$, so there were 4 50-year periods --> 1950-4*50=1750.

_________________
##### General Discussion
Manager
Joined: 29 Aug 2010
Posts: 148
Schools: Wharton/Lauder - Class of 2013
WE 1: Project Management, Telecommunications
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

20 Sep 2010, 13:42
1
3
I just worked this one backwards until I reached 160. If the population increases by 50% then you're multiplying the previous number by 3/2. So to work backwards, divide by 3/2 (which is the same as multiplying by 2/3).

So we have:

1950: 810
1900: 810*(2/3) = 540
1850: 540*(2/3) = 360
1800: 360*(2/3) = 240
1750: 240*(2/3) = 160

Manager
Joined: 20 Jul 2010
Posts: 173
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

20 Sep 2010, 18:41
1
55 sec to work forward for C

160 -> 240 -> 360 -> 540 -> 810
Senior Manager
Joined: 25 Feb 2010
Posts: 264
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

20 Sep 2010, 12:43
4 50 yrs to reach 810
_________________
GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...
BSchool Moderator
Joined: 19 Feb 2010
Posts: 294
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

20 Sep 2010, 17:50
redjam wrote:
I just worked this one backwards until I reached 160. If the population increases by 50% then you're multiplying the previous number by 3/2. So to work backwards, divide by 3/2 (which is the same as multiplying by 2/3).

So we have:

1950: 810
1900: 810*(2/3) = 540
1850: 540*(2/3) = 360
1800: 360*(2/3) = 240
1750: 240*(2/3) = 160

How long did it take you to work it like that?
Manager
Joined: 29 Aug 2010
Posts: 148
Schools: Wharton/Lauder - Class of 2013
WE 1: Project Management, Telecommunications
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

21 Sep 2010, 06:35
cano wrote:
How long did it take you to work it like that?

Didn't specifically time myself but it wasn't longer than 2 mins. I would say around 1.5 mins. They are all numbers easily divisible by 3.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15946
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

13 Feb 2017, 22:40
Hi All,

While this is an older prompt, it's still a great example of 'exponential growth', which is a concept that still appears on the GMAT occasionally. You can answer this question rather easily by TESTing THE ANSWERS.

We're told that a population increases by 50 percent every 50 years and that the population in 1950 was 810. We're asked to find the year in which the population was 160.

IF....
the population was 160 in 1700 then...
the population was 240 in 1750 and...
the population was 360 in 1800 and...
the population was 540 in 1850 and...
the population was 810 in 1900

This is TOO EARLY (the population is supposed to hit 810 in 1950). Notice the pattern here though - if we just "shift" all of the values 50 years 'forward', then we'll hit 810 in 1950 (when the population in 1750 was 160).

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Director
Joined: 23 Jan 2013
Posts: 521
Schools: Cambridge'16
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

17 Jul 2017, 21:13
equation is

160*(3/2)^x=810
(3/2)^x=5
x=4, so 50*4=200 years ago

C
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

20 Jul 2017, 16:51
cano wrote:
The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?

A. 1650
B. 1700
C. 1750
D. 1800
E. 1850

We can create the following equation:

160(1.5)^n = 810

(3/2)^n = 810/160

(3/2)^n = 81/16

Since 3^4 = 81 and 2^4 = 16, we see that n must be 4 so that (3/2)^n = 81/16. However, here n represents the number of 50-year periods that it took for the population to increase from 160 to 810. Thus, the number of years was 4(50) = 200 for the population of 160 to reach a population of 810 in 1950. So, the population of 160 must have occurred in 1750.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 13986
Re: The population of a certain town increases by 50 percent every 50 year  [#permalink]

### Show Tags

23 Nov 2019, 01:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The population of a certain town increases by 50 percent every 50 year   [#permalink] 23 Nov 2019, 01:20
Display posts from previous: Sort by