Question

There are 179 students currently registered in CPS420. This final exam is graded out of 75. For the purposes of this question you can assume that all the grades are integers. If you know that at most 10 students will get a grade strictly below 20, what is the least number of final exams that will need to be graded to guarantee that at least 2 students in this class have the same grade in this final exam? Explain your answer.

Answer 1

Total number of students = 179.

Maximum grade that can be received = 75.

We assume the worst case and believe the 10 students get a grade strictly below 20.

So, number of students getting grades greater than equal to 20 = 179-10 = 169.

These students can get a grade from 20 to 75. So the range between which these students can get the grade = 75-20+1 = 56.

As there are only 56 possible grades, then the maximum number of final exams that need to graded so that no student gets same grade as the other will be = 56+10 = 66.

So, we can say that if we grade the final exam of 67 students, we can be sure that atleast 2 students have the same grade.

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