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

[spoiler]OA: d[/spoiler]

What is the best approach to solve this question?

I tried to pick an option such as 11,000 and then divide the remaining population by 10(considering the population of rest of the districts equal)

## Problem solving

##### This topic has expert replies

- vk_vinayak
- Legendary Member
**Posts:**502**Joined:**03 Jun 2008**Thanked**: 99 times**Followed by:**21 members

Let s be the smallest population of any district. Then the maximum population other districts could have is 10% more than s ie 1.1s. And there are 10 other such districtssakshis 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 that the least populated district could have?

a) 10,700

b) 10,800

c) 10,900

d) 11,000

e) 11,100

[spoiler]OA: d[/spoiler]

What is the best approach to solve this question?

I tried to pick an option such as 11,000 and then divide the remaining population by 10(considering the population of rest of the districts equal)

s + 1.1s * (10) = 132,000

12s = 132,000

s = 11,000

- VK

I will (Learn. Recognize. Apply)

I will (Learn. Recognize. Apply)

- GMATGuruNY
- GMAT Instructor
**Posts:**15533**Joined:**25 May 2010**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1901 members**GMAT Score:**790

Your approach is fine.sakshis 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 that the least populated district could have?

a) 10,700

b) 10,800

c) 10,900

d) 11,000

e) 11,100

[spoiler]OA: d[/spoiler]

What is the best approach to solve this question?

I tried to pick an option such as 11,000 and then divide the remaining population by 10(considering the population of rest of the districts equal)

To MINIMIZE the smallest population, we need to MAXIMIZE the other 10 populations.

Thus, each of the other 10 districts must have the maximum allowed population: 10% greater than the smallest population.

Since the total population of the city is 132,000 -- a multiple of 1,000 -- the correct answer choice is almost certainly a multiple of 1,000.

**Answer choice D: 11,000.**

Each of the other 10 districts = (132,000 - 11,000)/10 = 12,100.

Difference between the populations = 12,100 - 11,000 = 1100, which is 10% of the smallest population.

Success!

The correct answer is D.

Mitch Hunt

Private Tutor for the GMAT and GRE

[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.

For more information, please email me at [email protected].

Student Review #1

Student Review #2

Student Review #3

Private Tutor for the GMAT and GRE

[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.

For more information, please email me at [email protected].

Student Review #1

Student Review #2

Student Review #3