Population
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let x = the population of the district with the LOWEST population.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% 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
To MINIMIZE the population in the smallest district, we must MAXIMIZE the population of the other 10 districts.
IMPORTANT: No other district can exceed x by more than 10%.
So 1.1x = the MAXIMUM population of each of the other 10 districts.
The TOTAL population is 132,000, so we can write:
(population of smallest district) + (population of other 10 districts) = 132,000
Rewrite as: x + [(10)(1.1x)] = 132,000
Simplify: 12x = 132,000
x = 11,000
Answer: D
Cheers,
Brent
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi eitijan,
Certain Quant questions have built in shortcuts IF the answer choices are numbers and if certain other conditions are met. Here, we can TEST THE ANSWERS....
Logically, when a GMAT question asks you to figure out the LEAST or GREATEST value of something, then there are going to be restrictions on how the values will relate to one another. Here we have 11 cities; to make one as SMALL as possible, I'd think to make all of the others as LARGE as possible.
The answers:
10,700
10,800
10,900
11,000
11,100
Statistically, it's best to TEST either B or D first. D seems like an easier number to manipulate, so I'll TEST that one first.
IF the least city = 11,000
Then 10% greater would be 12,100
IF the other 10 cities are 12,100 each, then they would sum to 121,000
Add in the least city: 121,000 + 11,000 = 132,000
Since all the math that I've done matches the data that I was given....
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
Certain Quant questions have built in shortcuts IF the answer choices are numbers and if certain other conditions are met. Here, we can TEST THE ANSWERS....
Logically, when a GMAT question asks you to figure out the LEAST or GREATEST value of something, then there are going to be restrictions on how the values will relate to one another. Here we have 11 cities; to make one as SMALL as possible, I'd think to make all of the others as LARGE as possible.
The answers:
10,700
10,800
10,900
11,000
11,100
Statistically, it's best to TEST either B or D first. D seems like an easier number to manipulate, so I'll TEST that one first.
IF the least city = 11,000
Then 10% greater would be 12,100
IF the other 10 cities are 12,100 each, then they would sum to 121,000
Add in the least city: 121,000 + 11,000 = 132,000
Since all the math that I've done matches the data that I was given....
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Let's say that the least populous town has population p. To get everyone else as far as possible from this town, we'll make every OTHER town as big as it can be: 10% greater than the least populous town.
That means that we've got one town with p and ten towns with 1.1p, for a total of
p + 10*1.1p = 132,000
12p = 132,000
p = 11,000
and we're set!
That means that we've got one town with p and ten towns with 1.1p, for a total of
p + 10*1.1p = 132,000
12p = 132,000
p = 11,000
and we're set!
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let x = the population of the district with the LOWEST population.
To MINIMIZE the population in the smallest district, we must MAXIMIZE the population of the other 10 districts.
IMPORTANT: No other district can exceed x by more than 10%.
So 1.1x = the MAXIMUM population of each of the other 10 districts.
The TOTAL population is 132,000, so we can write:
(population of smallest district) + (population of other 10 districts) = 132,000
Rewrite as: x + [(10)(1.1x)] = 132,000
Simplify: 12x = 132,000
x = 11,000
Answer: D
Cheers,
Brent
To MINIMIZE the population in the smallest district, we must MAXIMIZE the population of the other 10 districts.
IMPORTANT: No other district can exceed x by more than 10%.
So 1.1x = the MAXIMUM population of each of the other 10 districts.
The TOTAL population is 132,000, so we can write:
(population of smallest district) + (population of other 10 districts) = 132,000
Rewrite as: x + [(10)(1.1x)] = 132,000
Simplify: 12x = 132,000
x = 11,000
Answer: D
Cheers,
Brent