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The Highest Grade (Posted on 2003-12-11) Difficulty: 3 of 5
I had someone tell me, after seeing what grade they got on several quizzes, that he got the highest grade (after rounding to the nearest percent) for that letter, for all 5 quizzes. Each quiz he took, he got a different letter grade on it.

When the grades are calculated for these quizzes, it is the number of questions you got right divided by the number of questions total on the quiz. Then the score is taken as a percent (the decimal is multiplied by 100) and then rounded to the nearest percent (.5 and above rounds up, below .5 rounds down)

The grading scale works so that:

100-90 A
89-80 B
79-70 C
69-60 D
0-59 F

What are the fewest number of questions possible on each quiz?

For example, if someone got 6 questions right out of 7 questions total, it would be 6/7 or about 85.7%, which rounds to 86, which isn't the highest B possible, (86 is not equal to 89) Since no number over 7 can be in the 88.5 up to 89.5 range, there couldn't have been exactly 7 questions on the quiz. There also couldn't have been 8 questions on the B quiz. 7/8 or 88 percent isn't the highest B possible; it's too low, and 8/8 or 100 percent is too high.

No Solution Yet Submitted by Gamer    
Rating: 3.4000 (5 votes)

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Solution re: or if all tests have the same amount of questions | Comment 11 of 15 |
(In reply to or if all tests have the same amount of questions by mike)

If each of the five quizzes would have a different number of questions...

Quiz: 1 question. Number correct: 1.  
           Grade A := 100
Quiz: 9 questions. Number correct: 8. 
           Grade B := ~88.88889 
Quiz: 14 questions. Number correct: 11.
           Grade C := ~78.57143 
Quiz: 13 questions. Number correct: 9.
           Grade D := ~69.23077
Quiz: 17 questions. Number correct: 10
           Grade F := ~58.62069

If each of the five quizzes would have the same number of questions...

Quiz: 61 questions. Number correct: 61.  
           Grade A  := 100
Quiz: 61 questions. Number correct: 54. 
           Grade B  := ~88.52459 
Quiz: 61 questions. Number correct: 48.
           Grade C  := ~78.68852 
Quiz: 61 questions. Number correct: 42.
           Grade D := ~68.85246
Quiz: 61 questions. Number correct: 36.
           Grade F := ~59.01639

  Posted by Dej Mar on 2008-02-17 15:07:29
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