Last visit was: 23 Apr 2026, 23:45 It is currently 23 Apr 2026, 23:45
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
cano
User avatar
BSchool Moderator
Joined: 19 Feb 2010
Last visit: 14 Dec 2015
Posts: 268
Own Kudos:
561
 [36]
Given Kudos: 76
Posts: 268
Kudos: 561
 [36]
The population of a certain town increases by 50 percent every 50 year 20 Sep 2010, 10:10
5
Kudos
Add Kudos
29
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

72% (02:08) correct 28% (02:19) wrong based on 502 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,802
Own Kudos:
810,901
 [19]
Given Kudos: 105,868
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,802
Kudos: 810,901
 [19]
The population of a certain town increases by 50 percent every 50 year 20 Sep 2010, 10:20
9
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
cano
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
Show more

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.

So, we are given that \(160*1.5^n=810\), where \(n\) is the number of 50-year periods;

\(160*(\frac{3}{2})^n=810\);

\((\frac{3}{2})^n=\frac{810}{160}\);

\((\frac{3}{2})^n=\frac{81}{16}\);

\((\frac{3}{2})^n=(\frac{3}{2})^4\);

\(n=4\), so there were 4 50-year periods;

Thus the population was 160 at year \(1950-4*50=1750\).

Answer: C.
User avatar
redjam
User avatar
Joined: 29 Aug 2010
Last visit: 02 Mar 2012
Posts: 147
Own Kudos:
41
 [11]
Given Kudos: 16
Concentration: Entrepreneurship
Schools:Wharton/Lauder - Class of 2013
WE 1: Project Management, Telecommunications
Posts: 147
Kudos: 41
 [11]
The population of a certain town increases by 50 percent every 50 year 20 Sep 2010, 13:42
4
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
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

Answer is C
General Discussion
User avatar
cano
User avatar
BSchool Moderator
Joined: 19 Feb 2010
Last visit: 14 Dec 2015
Posts: 268
Own Kudos:
561
Given Kudos: 76
Posts: 268
Kudos: 561
The population of a certain town increases by 50 percent every 50 year 20 Sep 2010, 17:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
redjam
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

Answer is C
Show more

How long did it take you to work it like that?
User avatar
saxenashobhit
User avatar
Joined: 20 Jul 2010
Last visit: 14 Nov 2013
Posts: 135
Own Kudos:
256
 [2]
Given Kudos: 9
Products:
My Reviews
Posts: 135
Kudos: 256
 [2]
The population of a certain town increases by 50 percent every 50 year 20 Sep 2010, 18:41
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
55 sec to work forward for C

160 -> 240 -> 360 -> 540 -> 810
User avatar
redjam
User avatar
Joined: 29 Aug 2010
Last visit: 02 Mar 2012
Posts: 147
Own Kudos:
41
 [1]
Given Kudos: 16
Concentration: Entrepreneurship
Schools:Wharton/Lauder - Class of 2013
WE 1: Project Management, Telecommunications
Posts: 147
Kudos: 41
 [1]
The population of a certain town increases by 50 percent every 50 year 21 Sep 2010, 06:35
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
cano
How long did it take you to work it like that?
Show more

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.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,777
Own Kudos:
13,047
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,777
Kudos: 13,047
The population of a certain town increases by 50 percent every 50 year 13 Feb 2017, 22:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.

Let's TEST Answer B: 1700

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).

Final Answer:
Show Spoiler
C

GMAT assassins aren't born, they're made,
Rich
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,710
 [1]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,710
 [1]
The population of a certain town increases by 50 percent every 50 year 20 Jul 2017, 16:51
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
cano
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
Show more


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.

Answer: C
avatar
shantanugaware
avatar
Joined: 02 Nov 2021
Last visit: 13 Nov 2024
Posts: 7
Own Kudos:
3
Given Kudos: 11
Posts: 7
Kudos: 3
The population of a certain town increases by 50 percent every 50 year 17 Apr 2022, 00:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
cano
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.

Answer: C.
Show more
Why do we multiply by 3/2 if the question asks for 50% increase? Why not 1/2?
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,777
Own Kudos:
13,047
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,777
Kudos: 13,047
The population of a certain town increases by 50 percent every 50 year 17 Apr 2022, 20:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shantanugaware
Bunuel
cano
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.

Answer: C.
Why do we multiply by 3/2 if the question asks for 50% increase? Why not 1/2?
Show more

Hi shantanugaware,

If you want to increase a number by 50% of itself, then there are a number of different ways to perform that calculation. For example, you could add the number to 50% of itself:

For example:
100 + (50% of 100) = 100 + 50 = 150

Or you could multiply the initial number by 3/2 or 1.5 (since either of those would be the total of the original number added to 50% of itself:

For example:
100(3/2) = 300/2 = 150
100(1.5) = 150

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

Contact Rich at: [email protected]
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,963
Own Kudos:
1,117
Posts: 38,963
Kudos: 1,117
The population of a certain town increases by 50 percent every 50 year 08 Oct 2025, 23:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109802 posts
Krunaal
Tuck School Moderator
853 posts