Data Sufficiency

DS pb # 116.

if 75% of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

1. 60 % of guests who ordered dessert also ordered coffee

2. 90% of the guests who ordered coffee also ordered dessert

the answer explanation assumes that each guest ordered either dessert or coffee but that is not given in the question, how can we assume that?

Anyways, can someone pls explain. Thanks

If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

1.) 60% of the guests who ordered dessert also ordered coffee.
2.) 90% of the guests who ordered coffee also ordered dessert.

Let D = total who ordered dessert.
Let C = total who ordered coffee.
Let B = total who ordered both dessert and coffee.
Plug in guests = 100.

Then D = .75*100 = 75.

Statement 1: 60% of the guests who ordered dessert also ordered coffee.
B = .6*75 = 45.
Not way to determine C.
Insufficient.

Statement 2: 90% of the guests who ordered coffee also ordered dessert.
.9C = B.
Not way to determine C.
Insufficient.

Statements 1 and 2 together:
.9C = 45.
C = 50.
Sufficient.

The correct answer is C.

The solution tells us the following:
45 ordered both coffee and dessert.
50-45 = 5 ordered only coffee.
75-45 = 30 ordered only dessert.
Thus, 100-45-5-30 = 20 ordered neither coffee nor dessert.
The solution does not assume that every guest ordered coffee or dessert. Given the values above, 20 ordered neither.