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Sets - Unhappy sets

by venmic » Thu Jun 30, 2011 10:13 pm
On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 55 percent of the sales representatives prefer to stay at Hotel XYZ and 45 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?

[spoiler]Answer: [ 51][/spoiler]

Can anyone help me out with this
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by Frankenstein » Thu Jun 30, 2011 10:34 pm
Hi,
Accommodations at XYZ - 18, ABC - 42
Preference at XYZ - 33, ABC - 27
If all the people preferring XYZ are accommodated in ABC, still there are (42-33) places left in ABC which should be given to the ones who prefer ABC. And all the ones accommodated at XYZ can be filled by the ones who prefer ABC.
So, minimum of (42-33) = 9 people will go to their preferred hotels. So, maximum of 60-9 = 51 cannot be accommodated in hotel they prefer.
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by vineeshp » Thu Jun 30, 2011 10:35 pm
30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 55 percent of the sales representatives prefer to stay at Hotel XYZ and 45 percent prefer to stay at Hotel ABC
translates to:

Given acco at XYZ = 30 percent of 60 = 18
Given acco at ABC = 42

Prefer to stay at XYZ= 55 percent = 33
Prefer ABC: 27

Question: Highest number of reps not given the hotel they prefer.
Maximize the mismatch.
What if all the 33 who prefer XYZ were given at ABC and all remaining were given at ABC.
This way 33 XYZ fans get ABC and 18 ABC fans get XYZ. So we get 51 as a possible answer.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by amit2k9 » Thu Jun 30, 2011 11:20 pm
using the table format here -

PXYZ PABC

XYZ ? 18

ABC ? 42

33 27 60 total

PABC preferred ABC and PXYZ preferred XYZ.

hence max for PABC = 18 and for PXYZ = 33

hence 18+33 = 51.
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