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6 replies to this topic

#1 puzzled

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Posted 08 March 2008 - 01:20 AM

A school has 200 students. These are special students, some of them ALWAYS tell the truth, and the rest of them NEVER tell the truth. Among the subject areas of math, science, and social studies, each student has one favorite. A survey was conducted, each student was asked three yes or no questions: “Do you like math the most?” “Do you like science the most?” “Do you like social studies the most?”

The results were as follows:

104 students said “yes,” they like math the most.
86 students said “yes,” they like science the most.
60 students said “yes,” they like social studies the most.

How many students tell the truth, and how many do not?
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#2 Duh Puck

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Posted 08 March 2008 - 01:57 AM

A school has 200 students. These are special students, some of them ALWAYS tell the truth, and the rest of them NEVER tell the truth. Among the subject areas of math, science, and social studies, each student has one favorite. A survey was conducted, each student was asked three yes or no questions: “Do you like math the most?” “Do you like science the most?” “Do you like social studies the most?”

The results were as follows:

104 students said “yes,” they like math the most.
86 students said “yes,” they like science the most.
60 students said “yes,” they like social studies the most.

How many students tell the truth, and how many do not?

Hmmmm ... I could be wrong, but my gut tells me that you would have to know the distribution of the favorites among the students. If every student liked math, the results would be different than if every student liked science. Right?
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#3 puzzled

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Posted 08 March 2008 - 02:02 AM

Hmmmm ... I could be wrong, but my gut tells me that you would have to know the distribution of the favorites among the students. If every student liked math, the results would be different than if every student liked science. Right?


In this problem you don't need to.
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#4 redshift

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Posted 08 March 2008 - 03:04 AM

In this problem you don't need to.

Spoiler for Solution

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#5 slinks

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Posted 08 March 2008 - 03:08 AM

I think it's like this?
Spoiler for It's the truth

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#6 Duh Puck

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Posted 08 March 2008 - 08:02 AM

Nice. I like it when the problem has a clear, simple, yet non-intuitive answer. Of course, I like it better when I think of that answer myself. I'll take what I can get. :)
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#7 puzzled

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Posted 08 March 2008 - 01:22 PM

Good work slinks. Good job redshift. :D
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