This is a little test of reasoning ability. I would prefer that for the first few days, only ID advocates post answers. These questions, and the underlying reasoning, are widely discussed on the internet, so you may have encountered them. If you have, I would appreciate knowing that fact. Also, for those who have seen them before, I would like to know how you did the first time you encountered them.
If anyone spots a typo or logical error, I’d appreciate hearing about is so it can be corrected.
The answers I’m looking for are in three parts:
First — yes or no — can the puzzles be solved by reason, assuming ordinary knowledge of the vocabulary. There are no tricks or unusual meanings involved.
Second, provide the answer.
Third, the provide the reasoning or proof.
Uncommon Descent frequently invokes logic and reason. this is a challenge to anyone who posts at UD. Feel free to post your answers on this thread or at UD.
Here are the questions:
1. [The original editor has been sacked. Re-Edited to straighten out the mess: The price of a cheeseburger is $2.20, the price of a plain hamburger plus the price of the added cheese.] A plain hamburger costs two dollars more than the added cheese. How much does a plain hamburger cost?
2. In Elbonia, one person in ten thousand has Ebola. A new test is so good that anyone who is infected will test positive. But three percent of uninfected people will also test positive. John, a citizen of Elbonia tests positive. What is the probability that John has Ebola?
3. I have a deck of picture cards. They have automobiles on one side and living things on the other side. I have looked through them, and I think they follow the following rule: if a card has a GM automobile on one side, it will have an animal on the other side. After shuffling, I deal out four cards.
Cat, Ford, Petunia, Chevy
What cards must I turn over to test my hypothesis?
4. William is tweeting Betty, but Betty is tweeting John. William is in love, but John is not. Is a person in love tweeting a person who is not in love?
5. Elbonia has invented a treatment for Psoriasis. During a recent blind test, of the patients who were given the treatment 197 improved and 95 did not.
Of the patients who were given a placebo, 45 improved and 20 did not.
Is the treatment effective?