Let us calculate the minimum number of people who get accommodations in hotels they prefer.
30% will be given hotel XYZ and 45% prefer hotel ABC.
Suppose all 30% who are given XYZ come from 45% of who prefer ABC.
So (45 - 30)% or 15% get ABC which they prefer.
70% will be given ABC.
So (70 - 15)% or 55% is available in ABC.
It has already been given that 55% prefer XYZ. Let all of them be fitted into ABC so as to minimize the number of people who get the hotels they prefer.
Or we get that only 15% get the hotels they prefer.
So 85% do not get the preferred hotels.
This amounts to 85% of 60 = 51.
So the maximum number of people who do not get accommodations they prefer is 51.
Hotels
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Rahul@gurome
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naremnaresh
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30% of 60 = 18 has to stay in ABC
70% of 60 = 42 has to stay in XYZ
55% of 60 = 33 prefer to stay in xyz
45% of 60 = 27 prefer to stay in ABC
consider that outof 33 (who prefer to stay in xyz) 18 are accomodated in ABC
count = 18(who do not get the accommodation they prefer)
the remaining 33-18 = 15 and 27 are accomodated in xyz. out of these 27 donot get there preferred choice.
so count = 18 + 27 = 45(who do not get accommodations they prefer)
45 is the correct answer.
70% of 60 = 42 has to stay in XYZ
55% of 60 = 33 prefer to stay in xyz
45% of 60 = 27 prefer to stay in ABC
consider that outof 33 (who prefer to stay in xyz) 18 are accomodated in ABC
count = 18(who do not get the accommodation they prefer)
the remaining 33-18 = 15 and 27 are accomodated in xyz. out of these 27 donot get there preferred choice.
so count = 18 + 27 = 45(who do not get accommodations they prefer)
45 is the correct answer.
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Rahul@gurome
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The first part of your solution is not correct.naremnaresh wrote:30% of 60 = 18 has to stay in ABC
70% of 60 = 42 has to stay in XYZ
55% of 60 = 33 prefer to stay in xyz
45% of 60 = 27 prefer to stay in ABC
consider that outof 33 (who prefer to stay in xyz) 18 are accomodated in ABC
count = 18(who do not get the accommodation they prefer)
the remaining 33-18 = 15 and 27 are accomodated in xyz. out of these 27 donot get there preferred choice.
so count = 18 + 27 = 45(who do not get accommodations they prefer)
45 is the correct answer.
It should be:
30% of 60 = 18 has to stay in XYZ.
70% of 60 = 42 has to stay in ABC.
What you have done is the reverse.
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Geva@EconomistGMAT
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The 3*3 table is usually a good way to get your head wrapped around a sets question such as this one. Check out the attached table, with "XYZ / ABC in the rows and "prefer XYZ" / "Prefer ABC" in the columns. In order to maximize the number of people who get do not get the accommodation they want, we want to maximize the green boxes. Since there's no other limitation in the question, there's nothing stopping the green boxes from being the maximum of their respective row/column: 18+33=51.N:Dure wrote:??
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