Population

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Juggernaut_86: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Mon Feb 15, 2010 3:40 pm

by Juggernaut_86 » Mon Sep 05, 2011 5:59 pm

A certain city with a population of 132000 is to be distributed into 11 voting districts, and no district is to have a population that is more than 10% greater than the population of any other district. What is the minimum population that the least populted district could have?

(A)10700
(B)10800
(C)10900
(D)11000
(E)11100

OA - D

Could anyone please explain a quick way to solve this under 3 minutes?

Thanks!

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Source: Beat The GMAT — Problem Solving | Mon Sep 05, 2011 5:59 pm

edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Mon Sep 05, 2011 6:11 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Sep 05, 2011 6:45 pm

Juggernaut_86 wrote:A certain city with a population of 132000 is to be distributed into 11 voting districts, and no district is to have a population that is more than 10% greater than the population of any other district. What is the minimum population that the least populted district could have?

(A)10700
(B)10800
(C)10900
(D)11000
(E)11100

OA - D

Could anyone please explain a quick way to solve this under 3 minutes?

Thanks!

Let the 11 voting districts have populations d1, d2, d3, d4,....d11 respectively.
Let d1 be the least population.
So, d1+d2+d3+...+d11 = 132,000.
Now, according to question d2 <= 1.1*d1, d3 <= 1.1*d1,....d11<=1.1*d1.
Adding all inequality, we get that (d2+d3+d4...d11) <= 10*1.1*d1.
Or (d2+d3+d4...d11) <= 11d1.
Or (d1+d2+...+d11) <= 12d1.
Or 132,000 <= 12d1.
Or d1 => 11,000.
So, the minimum possible population of least populated district is 11,000.

The correct answer is D.

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Gurome, Inc.
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Juggernaut_86: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Mon Feb 15, 2010 3:40 pm

by Juggernaut_86 » Mon Sep 05, 2011 8:22 pm

Hi Anurag,

I understand the logic now. Thanks for replying.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Sep 05, 2011 8:24 pm

Juggernaut_86 wrote:Hi Anurag,

I understand the logic now. Thanks for replying.

You are welcome!

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mehrasa: Master | Next Rank: 500 Posts; Posts: 279; Joined: Fri Nov 05, 2010 5:43 pmFollowed by: 1 member; Thanked: 15 times

by mehrasa » Mon Sep 05, 2011 9:01 pm

so this means that the population of d1=11000 and the other regions all have the same population =1.1d1
does it make sense? i can,t undrestand

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

by saketk » Tue Sep 06, 2011 9:33 am

Juggernaut_86 wrote:A certain city with a population of 132000 is to be distributed into 11 voting districts, and no district is to have a population that is more than 10% greater than the population of any other district. What is the minimum population that the least populted district could have?

(A)10700
(B)10800
(C)10900
(D)11000
(E)11100

OA - D

Could anyone please explain a quick way to solve this under 3 minutes?

Thanks!

Hi - Although you got an excellent reply from Anurag, i'll try to explain what i did.

work with small numbers -- I took 132 only.

132/11 = 12 i.e. if all states have to have the same population, it will be 12

10% of 12 is 1.2
also, 12-1.2 = 10.8
But, if we keep the population of one state = 10.8 then other states will have to share the remaining 1.2 part.. that will clearly violate the condition (Population not more than 10%)
So our answer has to be bigger than 10.8 -- This eliminates option A & B.
Also, if you see the option C, it is very close to option B. So I parked this choice for some time.
Then I jumped to the next choice i.e. 11000.

if i put 11 as the population of 1 state.. other states will have to share the remaining (121 in this case)-- 132-11 = 121.. that mean the population of remaining 10 states will be 12.1 each. And 10% of 11 is 1.1

Hurrah!

This satisfies the constraint given in the question. CORRECT answer: - D

I used timer here and took exactly 2 mins to solve this one.. I think i did OK.

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