2000 AMC 12 Problem 13

Measure amounts in $8$-ounce cups, so Angela’s cup holds $c$ coffee and $m$ milk with $c + m = 1.$ Since Angela drank a sixth of the coffee, the total coffee is $6c$; since she drank a quarter of the milk, the total milk is $4m.$ The number of people equals the total number of cups, $$\begin{aligned} 6c + 4m &= 6c + 4(1 - c) \\ &= 4 + 2c. \end{aligned}$$ This is an integer only when $2c$ is an integer, and since $0 \lt c \lt 1$ this forces $c = \tfrac12,$ giving $4 + 1 = 5$ people. Thus, the correct answer is C.