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

Question

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

Actual

30% of 60 = 18 (IN XYZ)
70% of 60 = 42 (IN ABC)

Preference-

55% - 33 in XYZ
45% - 27 in ABC

18 at Hotel ABC XYZ be shifted to ABC

33 out of 42 at hotel ABC can be shifted to XYZ

18+33= 51.

MAXIMUM IS 51

A 11
B 18
C 36
D 45
E 51

soumanag · Accepted Answer

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.

mainhoon · Answer

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

zisis · Answer

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...

Bunuel · Answer

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PareshGmat · Answer

.................. ABC ...................... XYZ .................. Total

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

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

18 + 33 = 51

Answer = E

EMPOWERgmatRichC · Answer

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

Final Answer:  E

GMAT assassins aren't born, they're made, 
Rich

Krabhay · Answer

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

alwaysHP · Answer

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

Actual

30% of 60 = 18 (IN XYZ)
70% of 60 = 42 (IN ABC)

Preference-

55% - 33 in XYZ
45% - 27 in ABC

18 at Hotel ABC XYZ be shifted to ABC

33 out of 42 at hotel ABC can be shifted to XYZ

18+33= 51.

MAXIMUM IS 51

A 11
B 18
C 36
D 45
E 51

Actual

30% of 60 = 18 (IN XYZ)
70% of 60 = 42 (IN ABC)

Preference-

55% - 33 in XYZ
45% - 27 in ABC
 
 18 at Hotel ABC XYZ be shifted to ABC

33 out of 42 at hotel ABC can be shifted to XYZ

18+33= 51.

MAXIMUM IS 51

jainil7 · Answer

The total number of disappointed representatives is:
$$18 	ext{ (Prefer ABC at XYZ)} + 33 	ext{ (Prefer XYZ at ABC)} = \mathbf{51}$$
Final Answer: E
The highest possible number of sales representatives not given their preferred accommodation is 51.

jainil7 · Answer

Let's look at the limits for each:
 
  Group 1 (Prefer XYZ, put in ABC): 
There are 33 people who prefer XYZ. There are 42 spots in Hotel ABC.
Can all 33 be put in ABC?  Yes , because $33 \leq 42$.
 
  Unhappy people from this group:   33   
 
  Group 2 (Prefer ABC, put in XYZ): 
There are 27 people who prefer ABC. There are 18 spots in Hotel XYZ.
Can all 27 be put in XYZ?  No , because there are only 18 spots.
The maximum number of people from this group we can put in XYZ is 18.

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