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Grouping of students question

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by sensei_mike » Tue Dec 21, 2010 9:49 am
Hey Guys,

Here is the practice question I came across in the Kaplan Math workbook:
A class of 40 students is to be divided into smaller groups. If each group is to contain 3,4,or 5 people, what is the largest number of groups possible?

So I minimized the big groups to 1 each, and maxed the number of 3's groups but since there was a remainder, created 1 more group of 4, so 9 groups of 3. 2 groups of 4, 1 group of 5.

The OG however, says "each group must have at least 3 people in it" so create as many groups of 3 as possible. But that's NOT what the question says! The question says each group IS TO (i.e. must) contain 3,4 or 5 people.

Anyone else have the same line of thinking as me? Or should I be assuming even if it says "is to" that actually means "can but doesn't have to be"?
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Source: — Problem Solving |

by Rahul@gurome » Tue Dec 21, 2010 10:04 am
sensei_mike wrote:A class of 40 students is to be divided into smaller groups. If each group is to contain 3,4,or 5 people, what is the largest number of groups possible?

...should I be assuming even if it says "is to" that actually means "can but doesn't have to be"?
Yes.
Each group must contain either 3 or 4 or 5 students. There may not be any group with 3 students in it (or 4 or 5). All the groups may be of 4 students (or 5).

Only thing for sure the question tells us that there can't be any group of students with any other numbers of students in it.


Now for the problem we have to maximize the number of groups. Which means we have to minimize the number of students in each group.
  • Let's assume all the groups are of 3 students. 40 = (3*13 + 1) => A group of 1 student => NOT permissible.

    Let's assume all the groups are of either 3 or 4 students. Maximize groups of 3 and minimize group of 4. Say only one group of 4 => (4 + 12*3) = 40 => Permissible
Thus maximum numbers of groups possible = (12 + 1) = 13
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    by sensei_mike » Wed Dec 22, 2010 9:38 pm
    So going fwd I'm always going to go for the smallest possible amount and try for the larger groups being zero...Cool, thanks!
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