### Brain Teasers

# Slow and Stupid Wins the Race?

Hare and Tortoise had to take a make-up class in math over the summer, a two-month, self-paced 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 make-up class, after school in the fall.

How did Tortoise pass while Hare flunked?

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 make-up class, after school in the fall.

How did Tortoise pass while Hare flunked?

### Hint

They worked at different speeds.### 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

sigh.......

wierd

Very challenging teaser....awesome!

Good! I didn't get it

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.

If my math had been better, I'd have got it faster!!

Great MATH teaser!!

Great MATH teaser!!

awesome

Fun working this one out.

Great one, although I didn't get it right next time hopefully

I loved it!

++very++ nice

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!

the answer is already in the hint: They worked at different speeds!

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!

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!

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.

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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