1. If no head injury is too trivial to be neglected, then: if you injure your head, consult a physician. don't consult a physician no matter how trivial your head injury may be. don't injure your head unless you consult a physician. if you don't consult a physician, your head injury must be trivial.

2. Only one of the following sentences cannot be disambiguated to parse as a grammatical, meaningful sentence in English, using standard grammatical rules. Which one is the agrammatical sentence? The horse raced past the barn fell jumped. The rat the cat the dog chases hunts hides. Buffalo buffalo buffalo buffalo. The claim the horse he entered was a ringer was false.

3. Consider this simple syllogism. '(1) All artists are beekeepers. (2) Some beekeepers are chemists.' If (1) and (2) are both true, then which of the following must be true? None of the other options is correct. Some chemists are artists. Some artists are chemists. Some chemists are not artists.

4. Three cards are in a hat. One is red on both sides, one is white on both sides, and one is red on one side and white on the other. I draw a card from the hat, and drop it on the table. The upward-facing side is red. What is the probability that the downward-facing side is also red? Two out of three. One out of three. Fifty percent. None of the other options is correct.

5. Tom, Dick and Harry are in prison. One of them has been randomly selected to die in the morning, and the other two will be set free. Their guard knows which one will die, but none of the prisoners does. The guard is under strict instructions not to divulge the identity of the doomed man. Tom is desperate for any information beyond the fact that his probability of death is one in three. He begs the guard to throw him an informational bone. Finally, to shut him up, the guard agrees to reveal only the following: the name of one of Tom's fellow prisoners who will be set free rather than killed. The guard then says that Dick will be set free. After receiving this information from the guard, what is the most accurate calculation Tom can make of the probability that he is the doomed man? One out of two. None of the other options is correct. Two out of three. One out of three.