Asad wrote:
28 students were each assigned to one of five classes: Anthropology, Biology, Geology, Musicology, and Sociology. Was at least one of the classes assigned fewer than 5 students?
(1) At least 6 students were assigned to each of Biology, Geology, and Sociology.
(2) Geology and Sociology were not assigned the same number of students.
Solution
Step 1: Analyse Question Stem
• The number of students is 28.
• Each student is assigned to one of the classes of Anthropology, Biology, Geology, Musicology, and Sociology
• We need to find if at least one of the classes has fewer than 5 students.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: At least 6 students were assigned to each of Biology, Geology, and Sociology.
• The number of students in the Biology, Geology, and Sociology \(≥ 6\), but we do not know if the number of students in Anthropology and Musicology are less than 5. To understand this, let us consider two simple cases:
o Case 1: Let’s say each of the Biology, Geology, and Sociology has 6 students. Then, the number of students left \(28 -18 = 10\), hence each one of the Anthropology and Musicology can have 5 students.
Thus, no class has fewer than 5 students.
o Case 2: Let’s say Biology, Geology, and Sociology has 7 students each.Then, the number of students left \(28 - 21 = 7\) In this case at least one of Anthropology and Musicology will have fewer than 5 students.
The results of the above two cases are contradictory.
Hence, statement 1 is not sufficient and we can eliminate answer options A and D.
Statement 2: Geology and Sociology were not assigned the same number of students.
From this statement, we are not getting any information about the number of students in any of the classes.
Step 3: Analyse Statements by combining.
• From statement 1: The number of students in the Biology, Geology, and Sociology \(≥ 6\)
• From statement 2: Geology and Sociology were not assigned the same number of students.
• On combining both the statements: number of students in Biology, Geology, and Sociology\(≥ 6+6+7\)
o the number of students in Biology, Geology, and Sociology\(≥ 19\)
Hence, the number of students in Anthropology and Musicology \(≤ 9\)
Thus, at least one of the class will have fewer than 5 students.
Thus, the correct answer is
Option C.