Last visit was: 04 Nov 2024, 22:51 It is currently 04 Nov 2024, 22:51
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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
PREVIOUS TOPIC
NEXT TOPIC

Town A has a population of 160,000 and is growing at a rate

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
sandy
Retired Moderator
Joined: 07 Jun 2014
Posts: 4813
Own Kudos [?]: 11136 [6]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
Town A has a population of 160,000 and is growing at a rate [#permalink] New post   30 Jul 2018, 10:31
2
Expert Reply
4
Bookmarks
00:00

Question Stats:

75% (01:44) correct 24% (01:44) wrong based on 267 sessions

Hide Show timer Statistics

Town A has a population of 160,000 and is growing at a rate of 20% annually. Town B has a population of 80,000 and is growing at a rate of 50% annually.

Quantity A
Quantity B
The number of years until town B’s population is greater than that of town A
3


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
ShowHide Answer
Official Answer
A
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [4]
Given Kudos: 136
Send PM

Top Member of the Month
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   04 Aug 2018, 06:02
4
sandy wrote:
Town A has a population of 160,000 and is growing at a rate of 20% annually. Town B has a population of 80,000 and is growing at a rate of 50% annually.

Quantity A
Quantity B
The number of years until town B’s population is greater than that of town A
3


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Let's keep track of each population for 3 years

TOWN A
Present Population: 160 (we'll drop the 000's at the end for both populations)
Population in 1 year: (160)(1.2)
Population in 2 years: (160)(1.2)(1.2)
Population in 3 years: (160)(1.2)(1.2)(1.2) = (160)(1.2)³

TOWN B
Present Population: 80
Population in 1 year: (80)(1.5)
Population in 2 years: (80)(1.5)(1.5)
Population in 3 years: (80)(1.5)(1.5)(1.5) = (80)(1.5)³

Now that we know the populations after 3 years, we can check whether or not 3 years is enough time for Town B's population to exceed Town A's population.
So, let's examine the fraction: (160)(1.2)³/(80)(1.5)³

There are 3 possible cases:
case a) (160)(1.2)³/(80)(1.5)³ = 1, in which case, the 2 populations are EQUAL
case b) (160)(1.2)³/(80)(1.5)³ < 1, in which case, Town A's population is LESS THAN Town B's population
case c) (160)(1.2)³/(80)(1.5)³ > 1, in which case, Town A's population is GREATER THAN Town B's population

160/80 = 2 and (1.2)³/(1.5)³ = (1.2/1.5)³ = (12/15)³ = (4/5)³ = 64/125
So, (160)(1.2)³/(80)(1.5)³ = (2)(64/125) = 128/125
Since 128/125 > 1, we have a case c situation.
So, after 3 years, Town A's population is still GREATER THAN Town B's population
So, it will take MORE THAN 3 YEARS for Town B's population to exceed Town A's population

We get:
Quantity A: MORE THAN 3 YEARS
Quantity B: 3 years

Answer: A

Cheers,
Brent
avatar
ajbozdar
Retired Moderator
Joined: 31 Jul 2018
Posts: 32
Own Kudos [?]: 15 [1]
Given Kudos: 0
GPA: 3.07
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   06 Aug 2018, 00:26
1
I solved this question on paper, and it took me 05 minutes 20 seconds to get the answer. I went through the traditional percentile method year by year. The answer was right, but I am worried about taking a long time to solve it.
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 29887
Own Kudos [?]: 36114 [3]
Given Kudos: 25918
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   06 Aug 2018, 01:38
3
Expert Reply
In that time you should solve almost 3 questions not one only.

The Brent's approach above is fine and i do not think there is a shortcut. Sometimes you have to go through the question step by step moving fast.

Notice how B is 1/2 of A. So A could be written as 2 for simplicity and B = 1

2*1.2=2.4*1.2=2.8*1.2=3.4*1.2=4.14

1*1.5=1.5*1.5=2.25*1.5=3.37*1.5=5.06

Consider that you do have the calculator and the question to solve will end up in 30 seconds.

Hope this helps
avatar
ajbozdar
Retired Moderator
Joined: 31 Jul 2018
Posts: 32
Own Kudos [?]: 15 [0]
Given Kudos: 0
GPA: 3.07
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   07 Aug 2018, 03:48
Carcass wrote:
In that time you should solve almost 3 questions not one only.

Consider that you do have the calculator and the question to solve will end up in 30 seconds.



This was helpful, and I am working on to improve my skills. I lack of mathematical tricks, though.
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 29887
Own Kudos [?]: 36114 [0]
Given Kudos: 25918
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   07 Aug 2018, 14:13
Expert Reply
Use this

Regards

Attachment:
GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]
Downloaded 171 times
User avatar
sandy
Retired Moderator
Joined: 07 Jun 2014
Posts: 4813
Own Kudos [?]: 11136 [4]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   12 Aug 2018, 06:04
4
Expert Reply
Explanation

Set up a table and calculate the population of each town after every year; use the calculator to calculate town A’s population. If you feel comfortable multiplying by 1.5 yourself, you do not need to use the calculator for town B. Instead, add 50% each time (e.g., from 80,000 add 50%, or 40,000, to get 120,000).
Town ATown B
Now160,00080,000
Year 1160,000(1.2) = 192,00080,000 + 40,000 = 120,000
Year 2192,000(1.2) = 230,400120,000 + 60,000 = 180,000
Year 3230,400(1.2) = 276,480180,000 + 90,000 = 270,000


Note that, after three years, town A still has more people than town B. It will take longer than 3 years, then, for town B to surpass town A, so Quantity A is greater.
avatar
venom004
Intern
Intern
Joined: 14 Aug 2019
Posts: 8
Own Kudos [?]: 49 [0]
Given Kudos: 0
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   08 Oct 2019, 00:46
2
Well I combined the two approaches-

1) Drop all the zeros
2) Use the table

.............. Town A.....................Town B
Now......... 16 ..........................8
Year......... 16(1.2) = 19.2 ............8 + 4 = 12
Year 2....... 19.2(1.2) = 23.04 ........12 + 6= 18
Year 3....... 23.04(1.2) = 27.6.........18+ 9 = 27

So, at the end of year 3, the population of town A is > town B. Therefore, Quantity A is greater.
avatar
dodo2301
Intern
Intern
Joined: 07 Nov 2019
Posts: 2
Own Kudos [?]: 4 [0]
Given Kudos: 0
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   22 Nov 2019, 04:35
1
Treat this question as a compound interest question.

You will get below relationship

160,000* (1+0.2)exponential variable a< 80, 000 * (1+0.5) exponential variable a
2* (1.2) exponential variable a < 1.5 * exponential variable a

put a= 3 first

LHS RHS

3.456 3.375

so to increase value of RHS we need to put a value greater than 3 . It means option A is greater.
avatar
B
Ash1313
Intern
Intern
Joined: 11 Dec 2020
Posts: 13
Own Kudos [?]: 17 [1]
Given Kudos: 41
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   13 Feb 2021, 04:11
1
Yes, there is no shortcut. However, since you don't need to come up with an accurate anwser and it's just quantity comparison as aforementioned by one of the fellows above, you can simply ignore the zeros and use the calculator to multiply each town's population by its growth rate three times. So, we have:

Town's B population after 3 years: 8 x 1.5 x 1.5 x 1.5 = 27
Town's A population after 3 years: 16 x 1.2 x 1.2 x 1.2 = 27.648

We can see that the population in town A is greater than town B. Hence the answer is A.
User avatar
D
KarunMendiratta
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3208 [2]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   13 Feb 2021, 06:01
1
1
Bookmarks
sandy wrote:
Town A has a population of 160,000 and is growing at a rate of 20% annually. Town B has a population of 80,000 and is growing at a rate of 50% annually.

Quantity A
Quantity B
The number of years until town B’s population is greater than that of town A
3


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Function for Town A = \(160,000 (1.20)^t\)

Function for Town B = \(80,000 (1.50)^t\)

Col. A: Population of B > Population of A
i.e. \(80,000 (1.50)^t\) > \(160,000 (1.20)^t\)
\(\frac{(1.50)^t}{(1.20)^t}\) > 2
\((1.25)^t\) > 2
t > 3

Col. B: 3

Col. A > Col. B

Hence, option B
avatar
masudahmed
Intern
Intern
Joined: 12 Apr 2024
Posts: 3
Own Kudos [?]: 1 [0]
Given Kudos: 8
Send PM
Town A has a population of 160,000 and is growing at a rate [#permalink] New post   19 Jun 2024, 09:44
KarunMendiratta wrote:
Function for Town A = \(160,000 (1.20)^t\)

Function for Town B = \(80,000 (1.50)^t\)

Col. A: Population of B > Population of A
i.e. \(80,000 (1.50)^t\) > \(160,000 (1.20)^t\)
\(\frac{(1.50)^t}{(1.20)^t}\) > 2
\((1.25)^t\) > 2
t > 3

Col. B: 3

Col. A > Col. B

Hence, option B

Can you plz provide more details of, how it is done !?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 29887
Own Kudos [?]: 36114 [0]
Given Kudos: 25918
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   19 Jun 2024, 14:09
Expert Reply
This discussion has several great answers from different users

See for example above https://gre.myprepclub.com/forum/town-a ... tml#p22768 if it is more clear to you
avatar
S
defender007
Manager
Manager
Joined: 03 Jul 2024
Posts: 77
Own Kudos [?]: 31 [1]
Given Kudos: 129
Send PM
Re: Town A has a population of 160,000 and is growing at a rate [#permalink] New post   15 Jul 2024, 01:18
1
We can simply use the relative percent increase or decrease in population per year and take 30% increase in population of B per year keeping the population of A constant to find the Number of years it takes to overtake population A. We can Simply use the calculator to do this problem.
Prep Club for GRE Bot
gmatclubot
Re: Town A has a population of 160,000 and is growing at a rate [#permalink]
15 Jul 2024, 01:18
Moderators:
adewale223
GRE Instructor
77 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1111 posts
VibhuAnurag
GRE Instructor
228 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact