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rakaisraka: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Mon Jul 06, 2015 2:46 am

Gmat Prep question

by rakaisraka » Wed Aug 19, 2015 11:39 am

In a city total population is 132,000, it needs to be divided into 11 voting zones and NO zone to have a population that is more than 10% greater than the population of any other zone.What is the minimum possible population that the least populated zone could have.

- 10,700
- 10,800
- 10,900
- 11,000
- 11,100

Answer s 11,000.
I cant get the answer. Please explain.
Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Aug 19, 2015 11:39 am

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

by Brent@GMATPrepNow » Wed Aug 19, 2015 11:51 am

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

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

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

Brent Hanneson - Creator of GMATPrepNow.com

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rakaisraka: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Mon Jul 06, 2015 2:46 am

by rakaisraka » Wed Aug 19, 2015 3:13 pm

Thanks Brent.

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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

by [email protected] » Wed Aug 19, 2015 3:41 pm

Hi rakaisraka,

Did you copy this question from a particular source? I ask because Brent's post contains the original prompt written in the proper format. Your 'version' sounds more a poorly transcribed copy. If the original source wrote the question in this way, then that is likely a theft of copy-written material.

As far as this prompt is concerned....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

Contact Rich at [email protected]

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rakaisraka: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Mon Jul 06, 2015 2:46 am

by rakaisraka » Wed Aug 19, 2015 3:47 pm

Hi, This was from the gmat prep exam i took. I was not able to copy it so had to write it. Did i miss anything. I know i changed district to zone

Thanks

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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