A report compares ten academic departments at a university.

Question

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 .

Bunuel · Accepted 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.

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 average student ages among departments with evening classes is greater than the range of average 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:  False

I29-73

findingmyself · Answer

True, True, 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.:  Economist, Computer science and engineering (3/5) have student age above university average

The range of student ages among departments with evening classes is greater than the range of student ages among departments without evening classes.:  Evening class yes, Range is 52.3-27.9 which is greater than 41.8-29.4

Every department that has both library access and international programs also has an above-average student age.: Philosophy is not meeting this criteria

Karanzzz11 · Answer

My problem is that we have average student age and not the number of students.
So how can I determine the first two as true

Bunuel · Answer

The statements compare  department averages , not student counts.

Majority check = how many departments’ averages are above 37.18. 
 Range check = spread between highest and lowest department averages.

So both are valid using averages alone.

A report compares ten academic departments at a university.

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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

True	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.
		The range of average student ages among departments with evening classes is greater than the range of average student ages among departments without evening classes.
		Every department that has both library access and international programs also has an above-average student age.

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A report compares ten academic departments at a university.

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615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards