Problem Solving

Hi swerve,

We're told that 30% of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70% will be given accommodations at Hotel ABC. However, 55% of the sales representatives prefer to stay at Hotel XYZ and 45% prefer to stay at Hotel ABC. We're asked for the highest possible number of sales representatives that were NOT given accommodations at the hotel they prefer. 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: A

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