highest possible number of sales representatives

uptowngirl92 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

are you sure the answer choices are right? I get 15???

uptowngirl92 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

Let's start by converting percents into numbers, since the final answer needs to be in number form.

18 will end up in XYZ
42 will end up in ABC

33 WANT to be in XYZ
27 WANT to be in ABC

Now, let's see what we can do to maximize customer dissatisfaction!

All 33 who want to be in XYZ can fit into ABC, so let's throw them over there - that's 33 unhappy customers.

There's only room for 18 people in XYZ, so sadly we can't make all the pro-ABC people unhappy - but we can certainly upset 18 of the 27 who want to be in ABC by putting them in XYZ instead - another 18 unhappy people.

33 + 18 = 51 people who won't get a good night's sleep - choose (E).