maths

[mrinal2100]

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

[shovan85]

IMO E

[shovan85]

IMO E

Number of SP can be accommodated in XYZ = 30% of 60 = 18
Number of SP can be accommodated in ABC = 70% of 60 = 42

Number of SP prefer XYZ = 55% of 60 = 33
Number of SP prefer ABC = 45% of 60 = 27

In order to get the maximum number of sales representatives NOT
given accommodations at the hotel they prefer,

we can push all preferring XYZ to ABC that is 33 and all preferring ABC to XYZ is 27.

But XYZ can host only 18 members so we have 33+18 = 51.

[goyalsau]

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

Great Question Buddy,
and shovan explained it pretty well