Among a group of students, 20 like mathematics, 15 like science, and 10 like both mathematics and science. If every student in the group likes at least one subject, what is the minimum number of students in the group?
In a group of friends, Alice is taller than Bob, Bob is taller than Carol, and Carol is taller than David. If Alice is not the tallest in the group, which of the following must be true?
If all fruits are vegetables and some vegetables are red, which of the following statements is necessarily true?
In a group of employees, 60% are women, 40% are managers, and 20% are both women and managers. If every manager is a woman, what percentage of the women are managers?
Among a group of friends, each person either speaks Spanish, French, or German. If 8 people speak Spanish, 6 people speak French, and 4 people speak German, what is the maximum number of people in the group?