A certain city with a population of 132,000 is to be divided : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 12:40

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Director
Joined: 03 Sep 2006
Posts: 879
Followers: 6

Kudos [?]: 766 [0], given: 33

A certain city with a population of 132,000 is to be divided [#permalink]

### Show Tags

27 Apr 2010, 08:59
4
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:53) correct 37% (01:33) wrong based on 108 sessions

### HideShow timer Statistics

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 [ 15.65 KiB | Viewed 7573 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7066

Kudos [?]: 92903 [11] , given: 10528

Re: GMAT PREP (PS) [#permalink]

### Show Tags

27 Apr 2010, 11:00
11
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.
_________________
Director
Joined: 03 Sep 2006
Posts: 879
Followers: 6

Kudos [?]: 766 [0], given: 33

Re: GMAT PREP (PS) [#permalink]

### Show Tags

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
Manager
Joined: 03 May 2010
Posts: 88
WE 1: 2 yrs - Oilfield Service
Followers: 12

Kudos [?]: 109 [2] , given: 7

### Show Tags

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!
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 408
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Followers: 8

Kudos [?]: 196 [5] , given: 50

Re: GMAT PREP PS [#permalink]

### Show Tags

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.
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Senior Manager
Joined: 08 Nov 2010
Posts: 417
WE 1: Business Development
Followers: 7

Kudos [?]: 105 [0], given: 161

Re: GMAT PREP (PS) [#permalink]

### Show Tags

28 Jan 2011, 10:56
Great explanations.

Thanks.
_________________
Senior Manager
Joined: 30 Aug 2009
Posts: 286
Location: India
Concentration: General Management
Followers: 3

Kudos [?]: 161 [0], given: 5

Re: percentages [#permalink]

### Show Tags

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.
Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 100
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 7

Kudos [?]: 135 [2] , given: 10

Re: percentages [#permalink]

### Show Tags

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
Joined: 14 Dec 2010
Posts: 57
Followers: 0

Kudos [?]: 2 [0], given: 4

Re: A certain city with a population of 132,000 [#permalink]

### Show Tags

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 Replies Last post
Similar
Topics:
19 A certain city with a population of 132,000 is to be divided into 11 v 4 02 Jan 2015, 10:27
18 Boomtown urban planners expect the city’s population to 7 03 Mar 2012, 12:57
3 A certain city with population of 132,000 is to be divided into 11 vot 4 04 Nov 2011, 11:19
442 A certain city with population of 132,000 is to be divided 35 02 Mar 2009, 19:52
4 A certain city with population of 132,000 is to be divided i 9 10 Oct 2008, 08:17
Display posts from previous: Sort by

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.