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On a business trip, 30 percent of 60 sales representatives will be

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On a business trip, 30 percent of 60 sales representatives will be  [#permalink]

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New post 29 Aug 2010, 06:12
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Question Stats:

63% (02:44) correct 37% (03:03) wrong based on 452 sessions

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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
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Re: On a business trip, 30 percent of 60 sales representatives will be  [#permalink]

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New post 29 Aug 2010, 08:41
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I think there are two ways to approach this problem. Both of them gives the same result - 51.

Lets define the equations

Assigned: 60 = 18 to XYZ + 42 to ABC

Preference: 60 = 33 of XYZ + 27 of ABC

method 1 : 33 who preferred XYZ can be assigned to ABC in which case 42-33 = 9 will be assigned to hotel of their preference => 60 - 9 = 51 will be assigned to hotel not preferred by them.

method 2 : 18 out of total 27 who preferred ABC can be assigned to XYZ which leaves 9 out people who are satisfied with the arrangement and are assigned to ABC. => 60 -9 = 51 are unsatisfied.
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Re: On a business trip, 30 percent of 60 sales representatives will be  [#permalink]

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New post 29 Aug 2010, 06:42
5
well in this case out of 60, 18 are given xyz and 42 abc.. however, 33 want xyz and 27 want abc.. so to make the most number of people dissatisfied.. we can dump 33 into abc and get 9 from the 27 to go to abc.. then dump the remaining 18 of the 27 to go to xyz.. so now 33+18 are unhappy.. that is 51
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Re: On a business trip, 30 percent of 60 sales representatives will be  [#permalink]

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New post 29 Aug 2010, 06:57
thanks....thats how i thought about it but was wondering if there is a different method/way of thinking through it....lets see if more people post...
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Re: On a business trip, 30 percent of 60 sales representatives will be  [#permalink]

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New post 06 Oct 2014, 07:30
zisis 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


very weird question....cannt even classify it...


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Re: On a business trip, 30 percent of 60 sales representatives will be  [#permalink]

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New post 08 Oct 2014, 02:06
.................. ABC ...................... XYZ .................. Total

Actual ......... 42 ......................... 18 ....................... 60

Prefer .......... 27 ......................... 33 ..................... 60

18 + 33 = 51

Answer = E
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Re: On a business trip, 30 percent of 60 sales representatives will be  [#permalink]

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New post 12 Feb 2018, 14:10
Hi All,

While this prompt is "thick" with data, the math involved isn't too bad (you just have to stay organized and label your work).

The first sentence gives us data about the number of reps (out of 60) who will stay at each hotel:

Hotel XYZ = (.30)(60) = 18 reps
Hotel ABC = the rest = 42 reps

Next, we're told about the PREFERENCES of the reps

Hotel XYZ = (.55)(60) = 33 reps PREFER to stay at this hotel
Hotel ABC = (.45)(60) = 27 reps PREFER to stay at this hotel

From this, we can clearly see that some of the reps (at least 15) who want to stay at XYZ will NOT get what they want because there are not enough spots.

We're asked for the MAXIMUM number of reps who would NOT be assigned to the hotel that they prefer....

Here, we're limited by the number of reps who COULD stay at each hotel.

There are only 18 'reservations' at Hotel XYZ, so we can shift 18 reps from ABC to XYZ (making 18 reps who DON'T get what they want).
Next, we can put the remaining 42 people in ABC (making 33 reps who DON'T get what they want and 9 who DO).

Total reps who DON'T get what they want = 18+33 = 51

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Re: On a business trip, 30 percent of 60 sales representatives will be  [#permalink]

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New post 18 Dec 2018, 23:43
30% of 60 sales representatives = 18 representatives are staying at XYZ.
Remaining 70% i.e. 42 representatives are staying at ABC.
55% i.e. 33 representatives prefer to stay at XYZ.
45% i.e. 27 representatives prefer to stay at ABC.
Maximum representative not staying at preferred place is when all 33 representatives who prefer to stay at XYZ are staying at ABC and only 9 representatives who prefer to stay at ABC are staying at ABC.
So, highest number = 33 + 18 = 51 representatives are not staying at their preferred place
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Re: On a business trip, 30 percent of 60 sales representatives will be   [#permalink] 18 Dec 2018, 23:43
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