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Arithmetic

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by BTGmoderatorRO » Sun Dec 24, 2017 8:53 am
A metropolitan area with 132,000 college-aged individuals needs to be split up into 11 smaller units for a project. Of thise 11 units, no unit should have a total number of individuals that exceeds any other unit by more than 10%. What can be the least possible number of college-aged individuals in this metropolitan area?

(A) 10,600
(B) 10,750
(C) 11,000
(D) 11,150
(E) 11,500

OA is C

What is the best mathematical approach to solve this?
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by Brent@GMATPrepNow » Sun Dec 24, 2017 12:36 pm
Roland2rule wrote:A metropolitan area with 132,000 college-aged individuals needs to be split up into 11 smaller units for a project. Of thise 11 units, no unit should have a total number of individuals that exceeds any other unit by more than 10%. What can be the least possible number of college-aged individuals in this metropolitan area?

(A) 10,600
(B) 10,750
(C) 11,000
(D) 11,150
(E) 11,500

OA is C

What is the best mathematical approach to solve this?
This is a very close version of the Official question here: https://www.beatthegmat.com/arithmetic-t299499.html
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
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by [email protected] » Sun Dec 24, 2017 4:29 pm
Hi Roland2rule,

As Brent has pointed out, this prompt is a 'lift' of an Official question (although the answers are slightly different).

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:
(A) 10,600
(B) 10,750
(C) 11,000
(D) 11,150
(E) 11,500

Let's start with the 'nicest' number among the 5 choices...

IF the least unit = 11,000
Then 10% greater would be 12,100
IF the other 10 units are 12,100 each, then they would sum to 121,000
Add in the least unit: 121,000 + 11,000 = 132,000

This is an exact match for what we were told, so this MUST be the answer.

Final Answer: C

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by GMATWisdom » Mon Dec 25, 2017 12:46 pm
Roland2rule wrote:A metropolitan area with 132,000 college-aged individuals needs to be split up into 11 smaller units for a project. Of thise 11 units, no unit should have a total number of individuals that exceeds any other unit by more than 10%. What can be the least possible number of college-aged individuals in this metropolitan area?

(A) 10,600
(B) 10,750
(C) 11,000
(D) 11,150
(E) 11,500

OA is C

What is the best mathematical approach to solve this?
If the minimum number is 100 then maximum number should not exceed 110
For making unit of 100 individuals minimum
all other units should be near to maximum number of 110.
For 10 units to have 110 individuals and
one unit to have 100 individuals
the total individuals become 1100+100=1200.
If total individuals are 1200 minimum unit has individuals=100
If total individuals are 3200 minimum unit has individuals
=3200*100/ 1200 = 1100
Hence option C
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