Official Solution: Bunuel
A report compares ten academic departments at a university. The table shows the number of research labs and lecture halls in each department, along with whether the department offers library access, evening classes, and international programs. It also shows the average student age in each department. Chain-wide averages are included where appropriate.
| Department | Research Labs | Lecture Halls | Library Access | Evening Classes | International Programs | Average Student Age |
| History | 4 | 6 | yes | no | no | 34.2 |
| Biology | 6 | 8 | no | yes | yes | 27.9 |
| Mathematics | 5 | 4 | yes | no | no | 31.6 |
| Engineering | 10 | 2 | yes | yes | no | 45.5 |
| Literature | 3 | 5 | yes | no | yes | 41.8 |
| Physics | 7 | 7 | no | yes | yes | 33.7 |
| Economics | 6 | 3 | yes | yes | no | 38.9 |
| Philosophy | 2 | 9 | yes | no | yes | 29.4 |
| Sociology | 5 | 0 | no | yes | no | 36.5 |
| Computer Science | 9 | 4 | yes | yes | yes | 52.3 |
| averages | 5.7 | 4.8 | — | — | — | 37.18 |
For each of the following statements, select
True if the statement can be verified to be true based on the information provided. Otherwise, select
False.
• A majority of the departments that have more research labs than the university-wide average also have a student age above the university-wide average. Average labs = 5.7. Departments with more labs: Biology (6), Engineering (10), Physics (7), Economics (6), Computer Science (9). Their ages: 27.9, 45.5, 33.7, 38.9, 52.3. Three of these (Engineering, Economics, Computer Science) are above 37.2, the overall average. That is 3 out of 5, a majority.
Answer:
True • The range of student ages among departments with evening classes is greater than the range of student ages among departments without evening classes. Departments with evening classes: Biology (27.9), Engineering (45.5), Physics (33.7), Economics (38.9), Sociology (36.5), Computer Science (52.3). Range = 52.3 − 27.9 = 24.4.
Departments without evening classes: History (34.2), Mathematics (31.6), Literature (41.8), Philosophy (29.4). Range = 41.8 − 29.4 = 12.4.
Since 24.4 > 12.4, the statement holds.
Answer:
True • Every department that has both library access and international programs also has an above-average student age. Departments with both library access and international programs: Literature (41.8), Philosophy (29.4), Computer Science (52.3). Literature and Computer Science are above 37.2, but Philosophy is below. Because not all qualify, the condition fails.
Answer:
FalseCorrect answer: A majority of the departments that have more research labs than the university-wide average also have a student age above the university-wide average.
"True"The range of student ages among departments with evening classes is greater than the range of student ages among departments without evening classes.
"True"Every department that has both library access and international programs also has an above-average student age.
"False"