Maths Question

Conology

Hi all you Maths experts
Here's a question I need help with
3 Students doing a test.
Which of these students ( A, B or C ) has the best results.... and why ??

Student A B C
Time in Seconds 180 180 180
Q's Answered 150 129 110
Q's Correct 100 80 77

Taking the TIME factor into account - Which student has performed the BEST - is it
C -who had a 70% score or -
A -who answered more correct questions than any other student but achieved only 67% correct rate.
Thank you

PaulieBoy

Nice question!
I know I am completely wrong but my take is let 150 questions answered be 100% as you don't give the amount of questions.
With that thinking A answered all questions and got 67% of them correct.
B answered 86% of the questions and got 53% right.
C answered 73% of the questions and got 51% right.
So I figure A did best, but I am probably wrong!

Yakuza

In any actual real-world test, the total mark is out of the total number of questions. A attempted all the questions but "only" got 100 correct out of 150 (if 150 is the max), he still got 100 correct. C only got 77 correct, the other 73 either wrong or not answered. To me, it's a no-brainer that A still performed better on the test.

Taking that to a logical extreme, if C attempted 1 question and got it correct, would you still say he was the best of the lot, even if 149 (again, assuming 150 is the max) questions were untouched??

You mention taking time into account, which would appear to be irrelevant as they all took the same time.

No maths required, really, in my opinion, just common sense.

Conology

Thanks for the replies,

Kids homework ??? - I'll have to work harder as my old school report used to say.

Yakuza

It could be argued that C might be more accurate, but I'd still say A will do best on the test!

MathsManiac

I would agree that it's A, but it really depends on the rules of the contest or test. For example, some multiple-choice tests have a penalty for an incorrect answer that doesn't apply if you leave the question unanswered. e.g. if there are four options in each question, you get three marks for a correct answer, lose 1 mark for a wrong answer and score 0 for leaving the question unanswered.

In this scoring system,
A scores 300 - 50 = 250
B scores 240 - 49 = 191
C scores 231 - 33 = 198.

A still does best, but B and C have reversed places.

If it was a bank of true/false questions, it could conceivably be scored as +1 for correct, -1 for incorrect, 0 for unanswered. This would give:
A scores 100 - 50 = 50
B scores 80 - 49 = 31
C scores 77 - 33 = 44.

A still wins, but C has almost caught up. The point is, there are circumstances in which the winner might not be the person with the highest number of correct answers. However, under the rules of most quizzes and tests, the greatest number of correct answers correct wins. So, while I wouldn't necessarily agree with Yakuza that "In ANY real-world test...", I would agree that this is true in MOST real-world tests.

Yakuza

Fair point, MM, I didn't account for tests with negative marking, the question didn't go into such detail in any case, so standard marking could be inferred.