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

It is currently 29 Aug 2014, 20:53

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:
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 893
Followers: 6

Kudos [?]: 115 [0], given: 33

A certain city with a population of 132,000 is to be divided [#permalink] New post 27 Apr 2010, 08:59
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

60% (01:55) correct 40% (01:48) wrong based on 61 sessions
A certain city with 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 grater 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-city-with-population-of-132-000-is-to-be-divided-76217.html
[Reveal] Spoiler: OA

Attachments

PS5.PNG
PS5.PNG [ 15.65 KiB | Viewed 4674 times ]

Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Expert Post
9 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25206
Followers: 3418

Kudos [?]: 25043 [9] , given: 2702

Re: GMAT PREP (PS) [#permalink] New post 27 Apr 2010, 11:00
9
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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 greater 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

As "no district is to have a population that is more than 10 percent greater than the population of any other district", then the populations of 11 districts should be in the range: x and 1.1x.

So we want to minimize x. To minimize x we should make only one district to have that # of population (minimum possible) and the rest 10 districts to have 1.1x # of population (maximum possible).

x+10*1.1x=132 --> 12x=132 --> x=11.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 893
Followers: 6

Kudos [?]: 115 [0], given: 33

Re: GMAT PREP (PS) [#permalink] New post 28 Apr 2010, 02:23
Bunuel wrote:
A certain city with 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 greater 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

As "no district is to have a population that is more than 10 percent greater than the population of any other district", then the populations of 11 districts should be in the range: x and 1.1x.

So we want to minimize x. To minimize x we should make only one district to have that # of population (minimum possible) and the rest 10 districts to have 1.1x # of population (maximum possible).

x+10*1.1x=132 --> 12x=132 --> x=11.

Answer: D.


Thanks! One more Kudo to you
2 KUDOS received
Manager
Manager
avatar
Joined: 03 May 2010
Posts: 89
WE 1: 2 yrs - Oilfield Service
Followers: 11

Kudos [?]: 65 [2] , given: 7

GMAT Tests User Reviews Badge
 [#permalink] New post 15 Jun 2010, 05:00
2
This post received
KUDOS
First thing to realize:

You want to minimize the lowest possible quantity. For this we need to maximize all the others, however, we are limited by the question which tells us the greatest qty can only be 10% greater than the minimum one. So if the minimum value is x, the maximum value is 1.1x

Now, here's the trick, and this may not occur to many people - if you want to minimize this lowest qty, the only way to do this is to set ALL the other 10 to the maximum value. This is because those 10 cannot take a value more than that, and any value below that would lead to a higher value of the minimum one.

So: x + 10*1.1x = 132000

=> 12x = 132000

=> x = 11000


Hope this helps!
5 KUDOS received
Senior Manager
Senior Manager
User avatar
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 410
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Followers: 7

Kudos [?]: 115 [5] , given: 50

Re: GMAT PREP PS [#permalink] New post 23 Aug 2010, 18:33
5
This post received
KUDOS
uzzy12 wrote:
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 greater than the population of any other district. What is the minimum possible population taht the least populated district could have?

A. 10,700
B. 10,800
C. 10,900
D. 11,000
E. 11,100


My attempt:

132,000 divided by 11 districts would give us 12,000 people on average. Also we need to keep a population of a district minimum within the condition that the population of the no district is greater than 10% of the population of the least populated district.

Hence forming equation we get

D1 + D2 + D3 + .....D11 = 132,000
Let us assume D1 is the least populated district. If we have to reduce the number of people in the district D1 to a minimum and bound to the condition, we should equally distribute the difference of the minimized population of D1 and the average population of D1 (12000) equally to the rest of the 10 districts.

Hence D2 will be equal to D3 = D4 = D5 = ....= D11. Let D2 be x and b be the population of D1
hence 10 * x + b = 132000

also we know that x <= 1.1 b. Let us take the boundary case - x = 1.1b

Hence the equation becomes 10 * 1.1 b + b = 132000
11b + b = 132000

12b = 132000 => b = 11000.

x = 12100. Hence the answer is 11,000 (D).

I hope my reasoning is sound and in understandable format.
_________________

:good Support GMAT Club by putting a GMAT Club badge on your blog :thanks

Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 422
WE 1: Business Development
Followers: 7

Kudos [?]: 34 [0], given: 161

GMAT ToolKit User GMAT Tests User
Re: GMAT PREP (PS) [#permalink] New post 28 Jan 2011, 10:56
Great explanations.

Thanks.
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 30 Aug 2009
Posts: 290
Location: India
Concentration: General Management
Followers: 2

Kudos [?]: 93 [0], given: 5

GMAT Tests User
Re: percentages [#permalink] New post 08 Jan 2012, 05:09
kotela wrote:
Can anyone please help me in solving this problem.......


lets assume all districts have same population = 132000/11 = 12000

Consider option C - 10900 as correct (POE method)

then 10900 is 1100 less than avg of 12000. Even if equally divided the population of others will be 12100 - which is 1200 more than 10900 and more than 10% of 10900. So we need a higher value

Eliminate A, B and C

D - 11000 - this is 1000 less than assumed avg 12000 and if equally divided population will be 12100 which is exactly 10% greater than 11000.
2 KUDOS received
Manager
Manager
User avatar
Status: Employed
Joined: 17 Nov 2011
Posts: 101
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 4

Kudos [?]: 76 [2] , given: 10

Re: percentages [#permalink] New post 11 Jan 2012, 04:34
2
This post received
KUDOS
Weighted averages... That would be my solution to the question.

Voting districts = 11

Total = 132,000

Now how do we get "the least" value.... We make one min and the rest of the district equal to each other. It is absolutely imperative that you understand this statement. If all the rest are maximum possible value only then will you get the least possible value for one voting district.

From here on in, it is just about setting up the equation:

Let minimum = a

So max value possible = (10/100)a + a

Now write the equation...

1 of minimum and 10 of maximum value so.....
1*a + 10*(a + 0.1a) = 132,000

Solve for a = 11,000
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Manager
Manager
avatar
Joined: 14 Dec 2010
Posts: 58
Followers: 0

Kudos [?]: 1 [0], given: 3

GMAT Tests User
Re: A certain city with a population of 132,000 [#permalink] New post 15 Jan 2012, 23:08
Thanks a lot..great explanation...
Re: A certain city with a population of 132,000   [#permalink] 15 Jan 2012, 23:08
    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
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 rigger 5 23 Oct 2005, 17:21
A certain city with a population of 132,000 is to be divided Dan 5 13 Aug 2005, 05:19
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  


cron

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®.