Find all School-related info fast with the new School-Specific MBA Forum

It is currently 26 Oct 2014, 00:44

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A certain city with a population of 132,000 is to be divided

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2006
Posts: 375
Followers: 1

Kudos [?]: 1 [0], given: 0

A certain city with a population of 132,000 is to be divided [#permalink] New post 02 Dec 2006, 10:38
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent reater than the population of any other district. What is the minimum possible population that the least populated district could have?
A) 10,700
B) 10,800
C) 10,900
D) 11,000
E) 11,100

Anyone got a quick way to solve this one?
Director
Director
avatar
Joined: 28 Dec 2005
Posts: 922
Followers: 2

Kudos [?]: 37 [0], given: 0

 [#permalink] New post 02 Dec 2006, 11:32
Use the formula for geometric progression and using approximations you can solve. I had to look it up also. Ans E?

I am surprised this was on GmatPrep. Are we expected to know these formulae? Maybe this is not the route expected by GMAT.

Sn = ( a1 - a1 r^n ) / ( 1 - r)

a1 = 1

r = 1/10

n = 11

If x is the least population: x(1+1/10+1/10^2...1/10^10) = 132000
x * (1-(1/10)^11)/(1-1/10) = 132000 I approximated 10^11 - 1 as 10^11.
Senior Manager
Senior Manager
avatar
Joined: 08 Jun 2006
Posts: 343
Location: Washington DC
Followers: 1

Kudos [?]: 14 [0], given: 0

 [#permalink] New post 02 Dec 2006, 11:43
Getting E

Population of one district = A
A will be minimum only when all other districts’ populations are more than 10% of A
So A + (110A/100)*10 = 132,000
A = 11,000
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2006
Posts: 375
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 02 Dec 2006, 12:19
This scared me a little when it came up - hope I dont get it on the GMAT
Senior Manager
Senior Manager
avatar
Joined: 23 May 2005
Posts: 266
Location: Sing/ HK
Followers: 1

Kudos [?]: 14 [0], given: 0

 [#permalink] New post 03 Dec 2006, 07:20
Help pls... I don't get it...

"A will be minimum only when all other districts’ populations are more than 10% of A" --> why??

I also don't follow the arithmetic... A + (110A/100)^10 = 132,000A = 11,000
_________________

Impossible is nothing

Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2006
Posts: 375
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 03 Dec 2006, 08:12
I'm also missing the arithmetic - someone help!
Director
Director
avatar
Joined: 28 Dec 2005
Posts: 922
Followers: 2

Kudos [?]: 37 [0], given: 0

 [#permalink] New post 03 Dec 2006, 14:12
Trying to explain:

Ok, according to this: Let's say district A has the minimum, then a district B cannot be more than 10% of A. ie: A+10/100A= 110/100A. Now it's given that "no district is to have a population that is more than 10 percent greater than the population of any other district", so for A being a minimum, this can only be satisfied when all of the other 10 districts are 10% more than A (if they were any higher, then they would be more than 10% of A) . Thus the equation that Anindya came up with.
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2006
Posts: 375
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 03 Dec 2006, 14:59
thanks hsampath

Why when I try to do it the long way does the sum of the 11 districts not equal 132000?

1st district = 11,000 Multiplying each by 110/100 or 1.1
2nd = 12100
3rd = 13310
4th = 14641
5th = 16105.10 ...........
11th = 25686.8359

The sum of these does not equal 132000?
Director
Director
avatar
Joined: 28 Dec 2005
Posts: 922
Followers: 2

Kudos [?]: 37 [0], given: 0

 [#permalink] New post 03 Dec 2006, 15:26
that's where I made a mistake also, the first time around. it's actually

1st district = 11,000 Multiplying each by 110/100 or 1.1
2nd = 11000* 1.1 = 12100
3rd = 11000 *1.1 = 12100 NOT (12100*1.1=13310)
4th = 11000 * 1.1 = 12100 NOT (13310*1.1)
etc

because think abt this, with your logic: 3rd district = 13310 which is greater than 10% of the 1st district. According to question, it cannot be more than 10% of any other district, including A. Thus, 3rd, or 4th or anything else can be a max of 110/100*A.

Is this clearer?
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2006
Posts: 375
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 03 Dec 2006, 15:41
Dont worry - I've been misreading the question - I was looking at it as if it were a progression with a difference of 10% between districts ie. District 1 = x
District 2 = x+10%
District 3 = (x+10%)+10%

Thanks for your patience guys!
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2006
Posts: 375
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 03 Dec 2006, 15:42
hsampath wrote:
that's where I made a mistake also, the first time around. it's actually

1st district = 11,000 Multiplying each by 110/100 or 1.1
2nd = 11000* 1.1 = 12100
3rd = 11000 *1.1 = 12100 NOT (12100*1.1=13310)
4th = 11000 * 1.1 = 12100 NOT (13310*1.1)
etc

because think abt this, with your logic: 3rd district = 13310 which is greater than 10% of the 1st district. According to question, it cannot be more than 10% of any other district, including A. Thus, 3rd, or 4th or anything else can be a max of 110/100*A.

Is this clearer?


I see you just posted before me - thank hsampath - I was tearing my hair out trying to see what was wrong with my working when I'd just read the question wrong. Will add that to error log!!!
Senior Manager
Senior Manager
avatar
Joined: 23 May 2005
Posts: 266
Location: Sing/ HK
Followers: 1

Kudos [?]: 14 [0], given: 0

 [#permalink] New post 04 Dec 2006, 08:59
Aaaaaaaaa..... Now I get it. Tricky tricky...

Thansk hsampath.

I still hope i don't get a question like that n my exam.... Ack!
_________________

Impossible is nothing

  [#permalink] 04 Dec 2006, 08:59
    Similar topics Author Replies Last post
Similar
Topics:
A certain city with a population of 132000 is to be divided shobuj40 3 10 Jan 2009, 01:42
A certain city with a population of 132,000 is to be divided GMATBLACKBELT 1 17 Oct 2007, 18:32
1 A certain city with a population of 132000 is to be divided tlntd42 6 29 Sep 2007, 09:55
A certain city with a population of 132000 is to be divided positive_energy 4 01 Aug 2006, 09:00
A certain city with population of 132,000 is to be divided ps_dahiya 6 30 Jul 2006, 20:23
Display posts from previous: Sort by

A certain city with a population of 132,000 is to be divided

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.