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Teams of People - One is Incomplete

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by beeparoo » Sun Jun 22, 2008 5:08 pm
Hi Guys... Here is my attempt at writing a PS problem.

A group of people, m, are divided into teams of n members. If all teams except one have an equal number of members, while the final incomplete team contains only 64% of the members of any complete team, then how many people are in the team containing the least number of people? Each team must contain less than 50 people.

A - 64
B - 32
C - 25
D - 16
E - 12
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by Nycgrl » Sun Jun 22, 2008 6:19 pm
Is ans D???
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by beeparoo » Sun Jun 22, 2008 6:55 pm
Nycgrl wrote:Is ans D???
YES! Answer is D

Way to go!
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by Nycgrl » Sun Jun 22, 2008 7:04 pm
I used back solving method.

it says that incomplete team consist of 64% of members of any team
let number of peopel on complete team be X

start with C= 25

64/100*X=25 X= 6.2..there can't be 6.2 people on team


check D=16

64/100*X=16

X=25


If you try any other number you will not get X= integer except 16.


There could be another method to solve this question....
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by beeparoo » Sun Jun 22, 2008 8:19 pm
Nycgrl wrote:There could be another method to solve this question....
Yes - there is! The other method I propose is to think of "the remainders" of imperfect divisions.

Your method works, NYCgrl. I hope it was clearly expressed. It took me an hour to craft the wording of it. I hope it didn't take longer than 2 min to solve either.

Really, this question could be solved in less than 20 sec.

I'll write a full explanation soon..
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by beeparoo » Mon Jun 23, 2008 12:04 pm
Here's the official solution:

m = total population
n = number of people in a complete team
t = number of complete teams, a whole number

m = nt + 0.64n
m = n*(t + 64/100)

Since t is a whole number, 64/100 represents the remainder as a percentage of a complete team.

(64/100) = (32/50) = (16/25)

Since question states that teams must contain less than 50 members, the remaining people who are put into the final, incomplete team, equals 16.

I hope it's clear... Let me know!
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