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02 Jun 2022, 12:30
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Difficulty:
45%
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Question Stats:
67% (01:39) correct
33%
(01:59)
wrong
based on 211
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The percentage of students with grade point averages higher than 3.0 in the English department is higher than the percentage in any other department. However, the percentage of students with grade point averages higher than 3.5 is highest in the Physics department.
If the statements above are true, which of the following must also be true?
A. The percentage of students with grade point averages higher than 3.7 is higher in the Physics department than it is in the English department.
B. The English department has the second highest percentage of students with grade point averages higher than 3.5.
C. Some students in the English department have grade point averages higher than 3.0 but lower than 3.5.
D. The English department has more total students than does the Physics department.
E. The average grade point average of the Physics department is higher than the average grade point average of the English department.
If the statements above are true, which of the following must also be true?
A. The percentage of students with grade point averages higher than 3.7 is higher in the Physics department than it is in the English department.
B. The English department has the second highest percentage of students with grade point averages higher than 3.5.
C. Some students in the English department have grade point averages higher than 3.0 but lower than 3.5.
D. The English department has more total students than does the Physics department.
E. The average grade point average of the Physics department is higher than the average grade point average of the English department.
02 Jun 2022, 22:48
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Premise:
1. % of students with GPA > 3.0 is highest in English department.
2. % of students with GPA > 3.5 is highest in the Physics department.
Analysis: This implies that English department has highest % of students in the range of 3 to 3.5, while Physics department has highest % of students in the range > 3.5
e.g., lets say English Department has 80% students with GPA = 3.1 and 20% students with GPA = 3.8.
And, say Physics department has 80% students with GPA = 3.6 and 20% students with GPA = 1.
A. The percentage of students with grade point averages higher than 3.7 is higher in the Physics department than it is in the English department.
--> For given conditions to be true, we can have no student with GPA > 3.7 in Physics department, while few students having GPA > 3.7 in English department.
B. The English department has the second highest percentage of students with grade point averages higher than 3.5.
--> With above conditions, we can have a third department with 30% students having GPA = 3.6. Now, this department will be the second highest % of students with GPA > 3.5
C. Some students in the English department have grade point averages higher than 3.0 but lower than 3.5.
--> This must be true as English department should have students with GPA > 3.0. Only the % of students having GPA >3.5 should not be greater than % of students in Physics department having GPA > 3.5.
D. The English department has more total students than does the Physics department.
--> This need not be true. Because we are looking at only the percentages of students, we can have 10,000 students in Physics department and only 100 students in English department, while the percentages agree with premise.
E. The average grade point average of the Physics department is higher than the average grade point average of the English department.
--> Let's say, In English department let 100 students have GPA = 3.45. So the average GPA = 3.45.
And say, In Physics department 50 students have GPA=3.6 and 50 students have GPA=1.6. So the average GPA is 2.6.
So, avg(Eng dept) > avg(Physics dept).
This dataset satisfies all the premises: % of students in English department having GPA > 3 is highest = 100%, and GPA >3.5 = 0%
While, % of students in Physics department having GPA > 3.5 is highest = 50%, and GPA >3.0 = 50%
Hence E need not be true always.
1. % of students with GPA > 3.0 is highest in English department.
2. % of students with GPA > 3.5 is highest in the Physics department.
Analysis: This implies that English department has highest % of students in the range of 3 to 3.5, while Physics department has highest % of students in the range > 3.5
e.g., lets say English Department has 80% students with GPA = 3.1 and 20% students with GPA = 3.8.
And, say Physics department has 80% students with GPA = 3.6 and 20% students with GPA = 1.
A. The percentage of students with grade point averages higher than 3.7 is higher in the Physics department than it is in the English department.
--> For given conditions to be true, we can have no student with GPA > 3.7 in Physics department, while few students having GPA > 3.7 in English department.
B. The English department has the second highest percentage of students with grade point averages higher than 3.5.
--> With above conditions, we can have a third department with 30% students having GPA = 3.6. Now, this department will be the second highest % of students with GPA > 3.5
C. Some students in the English department have grade point averages higher than 3.0 but lower than 3.5.
--> This must be true as English department should have students with GPA > 3.0. Only the % of students having GPA >3.5 should not be greater than % of students in Physics department having GPA > 3.5.
D. The English department has more total students than does the Physics department.
--> This need not be true. Because we are looking at only the percentages of students, we can have 10,000 students in Physics department and only 100 students in English department, while the percentages agree with premise.
E. The average grade point average of the Physics department is higher than the average grade point average of the English department.
--> Let's say, In English department let 100 students have GPA = 3.45. So the average GPA = 3.45.
And say, In Physics department 50 students have GPA=3.6 and 50 students have GPA=1.6. So the average GPA is 2.6.
So, avg(Eng dept) > avg(Physics dept).
This dataset satisfies all the premises: % of students in English department having GPA > 3 is highest = 100%, and GPA >3.5 = 0%
While, % of students in Physics department having GPA > 3.5 is highest = 50%, and GPA >3.0 = 50%
Hence E need not be true always.
05 Sep 2023, 07:40
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