Slow and Stupid Wins the Race?
Math brain teasers require computations to solve.
Hare and Tortoise had to take a makeup class in math over the summer, a twomonth, selfpaced course with a test at the end of each of 12 chapters. The course requires a 70% grade to pass.
In the first month, they both had difficulties with the concepts. Hare averaged 60% on his exams; Tortoise averaged 50%. Owl, the supervisor, spent three days of the next week helping them with their difficulties.
It worked. In the second month, Hare averaged 90% on his exams; Tortoise averaged 80%.
However, Tortoise got a passing grade of 75% in the class; Hare failed with 65%. When Hare protested to Owl that he'd outscored Tortoise in both months, Owl made Hare do the math on the board  and sign up for another makeup class, after school in the fall.
How did Tortoise pass while Hare flunked?
HintThey worked at different speeds.
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Answer
In the first month, Hare took 10 chapter tests; Tortoise took only 2. In the second month, Hare took his remaining 2 exams and Tortoise took the 10 he needed to finish.
Hare's average = (10*60 + 2*90) / 12 = 780/12 = 65
Tortoise's average = (2*50 + 10*80)/12 = 900/12 = 75
Mathematicians know this as Simpson's paradox.
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Comments
Darklight
Sep 14, 2005
 sigh....... 
joeyleahs2
Sep 14, 2005
 wierd 
kayleeskitties
Sep 15, 2005
 Very challenging teaser....awesome! 
quickster94
Sep 20, 2005
 Good! I didn't get it 
mbunap
Sep 23, 2005
 Since you did not ask for the math behind the scores, I didn't bother to do it. It was obvious that Hare took most of his tests in the first month, while tortoise took his in the second month. Because of my approach, I questioned why this question was placed in the math category. If you had asked for the arithmatic behind the numbers, the math category would have seemed appropriate. Still fun. 
signmeup74
Oct 03, 2005
 If my math had been better, I'd have got it faster!!
Great MATH teaser!! 
lifeisgood812
Oct 10, 2005
 awesome 
zonarita
Oct 23, 2005
 Fun working this one out. 
redraptor50
Nov 13, 2005
 Great one, although I didn't get it right next time hopefully 
legodude
Apr 09, 2006
 I loved it! 
calmsavior
May 10, 2006
 ++very++ nice 
pating
Jun 19, 2007
 the question is "How did Tortoise pass while Hare flunked?", not "how to get their average grades after the 1st month or the 2nd month or for the whole class".
the answer is already in the hint: They worked at different speeds! 
MarcM1098
Jan 31, 2008
 Excellent quiz.
I guessed at the answer, but then did the MATH to show that I was right. A math test requires you to show your work, not just the answer! 
Jimbo
Jun 04, 2013
 It does not say that all of the chapter tests were worth the same value. The principle is simply that there was unequal weighting between the 2 sessions. This might have been because of a different number of tests or it might have been because the tests were out of different scores. In either case it is not statistically correct to simply average diversely weighted scores to come up with a summary mean. 
Jimbo
Jun 04, 2013
 To be clear I am not disputing the answer, just the fact that the implication that because Hare was higher on 2 separate tasks that he would be higher overall. 
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