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Percent problem

by selango » Thu Jun 24, 2010 10:28 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?
A) 11
B) 18
C) 36
D) 45
E) 51

OA E
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by singhpreet1 » Thu Jun 24, 2010 10:45 pm
selango wrote: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?
A) 11
B) 18
C) 36
D) 45
E) 51

OA E
hi Selango..are you sure about the answer choices and the OA?? also quote the source please.

30% of 60=18 who will be staying at XYZ.
70% of 60=42 who will be staying at ABC
55% of 60=33 prefer hotel XYZ
45% of 60=27 prefer hotel ABC

total number of sales representatives NOT given accommodations at the hotel they prefer: 33-18=15+ 42-27=15, 15+15= 30.

if i am going worng somewhere, please correct me.

Thanks, Preet.
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by kvcpk » Thu Jun 24, 2010 11:04 pm
Percentage calculations will return following results:

XYZ hotel has 18 people
ABC hotel has 42 people

33 prefer to stay in XYZ
27 prefer to stay in ABC

We are asked for the maximum number of people NOT given accommodations at the hotel they prefer

Assume that all the 33 people who prefered to stay in XYZ are placed in ABC.
Then ABC has 42-33=9 people who wanted to stay in ABC.

So out of 27 people who prefered to stay in ABC, 9 people are already in ABC.
Which means, 18 people are in XYZ.

so total is 33 + 18 = 51 people.


Hope this helps!!
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by amising6 » Thu Jun 24, 2010 11:53 pm
selango wrote: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?
A) 11
B) 18
C) 36
D) 45
E) 51

OA E
sales representatives will be given accommodations at Hotel XYZ=18
given accommodations at Hotel ABC=42
sales representatives prefer to stay at Hotel XYZ=33
45 percent prefer to stay at Hotel ABC=27

now let us assume that all given accomodation hotel at abc where those who prefered to stayat xyz =33
so prefernce wise thsoe who wanted to stay at xyz are 9
so in XYZ those who prefred to stay at abc=18
highest possible number of sales representatives NOT given accommodations at the hotel they prefer=33+18=51
cheers
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by gmatmachoman » Sat Jun 26, 2010 9:59 pm
kvcpk wrote:Percentage calculations will return following results:

XYZ hotel has 18 people
ABC hotel has 42 people

33 prefer to stay in XYZ
27 prefer to stay in ABC

We are asked for the maximum number of people NOT given accommodations at the hotel they prefer

Assume that all the 33 people who prefered to stay in XYZ are placed in ABC.
Then ABC has 42-33=9 people who wanted to stay in ABC.

So out of 27 people who prefered to stay in ABC, 9 people are already in ABC.
Which means, 18 people are in XYZ.

so total is 33 + 18 = 51 people.


Hope this helps!!

praveen bhai,

i am clueless!!Explain me more!!
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by kvcpk » Sun Jun 27, 2010 12:39 am
gmatmachoman wrote: praveen bhai,
i am clueless!!Explain me more!!
Ok Let me start again:

XYZ hotel has 18 people
ABC hotel has 42 people

33 prefer to stay in XYZ
27 prefer to stay in ABC

You would have understood till this point.

We want to know the maximum number of people not given accommodation at their preferred hotel.

ABC hotel has 42 people. How many of those 42 preferred not to stay in ABC? This we do not know.
We need to maximize this count as much as possible.
So to arrive at that point, we are assuming that the 33 people who preferred to stay in XYZ are all placed in ABC.

That brings us to say that 42-33=9 people, placed in ABC, actually preferred to stay in ABC.

How many people are we left with now - Who preferred to stay in ABC?
27 - 9 = 18 people are left who preferred to stay in ABC. But there is no place for them.
So they are placed in XYZ.
XYZ has all these 18 people. [it has no one who preferred to stay in XYZ]

Hence, Finally,
How many people are placed in ABC but prferred XYZ: 33
How many people are placed in XYZ but prferred ABC: 18

Total 18 + 33 = 51

Hope this helps, let me know if you have any issues.

Praveen
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by Testluv » Sun Jun 27, 2010 8:10 pm
received a pm.

kvcpk's solution is great.

Setting up chart may help to see things a bit more clearly:

-------------------XYZ------------------ABC
staying----------18--------------------42
prefer------------33-------------------27

We need to maximize the number of people who are staying at a hotel which they don't prefer.

Take all 33 who prefer XYZ, and put them in the ABC "staying" group....So, that's 33 so far.

There are 42 total staying in ABC. That leaves 18 staying in XYZ (as the chart shows). All 18 of these people could be among the 27 who would have preferred ABC. So, that could be another 18 staying in a hotel they don't prefer.

So, there could be up to 33 + 18 = 51 people staying in a hotel they don't prefer.

(kvcpk's solution was very similar: Once we place 33 who preferred XYZ into the ABC group, that leaves only 9 ABC-preferrers in the ABC group. Thus, the other 18 ABC-preferrers (27-9) must be in the XYZ group).
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