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 the total number of guests = 100.
Let:
D = the number who ordered dessert.
C = the number who ordered coffee.
B = the number who ordered BOTH.
Since 75% of the guests ordered dessert, we get:
D = 0.75 * 100 = 75.
Statement 1: 60% of the guests who ordered dessert also ordered coffee.
In other words, 60% of the 75 guests who ordered dessert ordered BOTH dessert AND coffee.
Thus:
0.6 * 75 = B
B = 45.
No way to determine the value of C.
INSUFFICIENT.
Statement 2: 90% of the guests who ordered coffee also ordered dessert.
In other words, 90% of the guests who ordered coffee ordered BOTH coffee AND dessert.
Thus:
0.9C = B.
No way to determine the value of C.
INSUFFICIENT.
Statements combined:
Since 0.9C = B and B = 45, we get:
0.9C = 45
C = 50.
SUFFICIENT.
The correct answer is
C.
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