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26 May 2017, 04:43
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A professor gives grades of A, B, C, D and F to the students, but he must give the students only one grade. If the professor needs to ensure that 6 students receive the same grade, what is the smallest possible number of students?
A. 6
B. 12
C. 24
D. 26
E. 30
A. 6
B. 12
C. 24
D. 26
E. 30
26 May 2017, 04:46
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Official Solution:
A professor gives grades of A, B, C, D and F to the students, but he must give the students only one grade. If the professor needs to ensure that 6 students receive the same grade, what is the smallest possible number of students?
A. 6
B. 12
C. 24
D. 26
E. 30
First, in order to confirm that all 6 students receive the same grade, we should consider the worst case in which 6 people do not get the same grade. In this case, it is where A, B, C, D, F is each given to 5 people. At this time, if there is one more student, there are already 5 students for each grade of A, B, C, D and F, so no matter what grade this student gets, the number of students who get the same grade will be 6. Hence, the table below is formed.
A grade B grade C grade D grade F grade Additional grade Number of Students 5 5 5 5 5 1
Just as the table above, 5 people received each of the grades A, B, C, D, and F. If one more student is added, that student receives one of the grades A, B, C, D, or F, and thus the number of students who received the same grade as that student is 6. Therefore, you get \(5 * 5 + 1 = 26\).
Answer: D
A professor gives grades of A, B, C, D and F to the students, but he must give the students only one grade. If the professor needs to ensure that 6 students receive the same grade, what is the smallest possible number of students?
A. 6
B. 12
C. 24
D. 26
E. 30
First, in order to confirm that all 6 students receive the same grade, we should consider the worst case in which 6 people do not get the same grade. In this case, it is where A, B, C, D, F is each given to 5 people. At this time, if there is one more student, there are already 5 students for each grade of A, B, C, D and F, so no matter what grade this student gets, the number of students who get the same grade will be 6. Hence, the table below is formed.
A grade B grade C grade D grade F grade Additional grade Number of Students 5 5 5 5 5 1
Just as the table above, 5 people received each of the grades A, B, C, D, and F. If one more student is added, that student receives one of the grades A, B, C, D, or F, and thus the number of students who received the same grade as that student is 6. Therefore, you get \(5 * 5 + 1 = 26\).
Answer: D
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