Based on the following description, answer the questions below:
Three students named Alice, Brittany, and Cheri each are enrolled in three of these four classes: Math, Biology, Chemistry, and History. When discussing their courses, each of them said the following:
Alice: There is only one subject we are all taking. I am the only one of us who is taking math. The same three classes are not being taken by any two of us. Cheri is wrong that Brittany and I both take chemistry.
Brittany: Alice is the only one of us taking history. Cheri and I are taking the same classes. All of us have a biology class. There are two of us taking both biology and history.
Cheri: All of us have a math class. Brittany is in a history course. Alice has one class that I don’t have. Alice and Brittany are both taking a chemistry class.
1. Assuming that only two of each student’s four statements are true, which courses is Alice taking?
A. Chemistry, biology, and history
B. Chemistry, biology, and math
C. Chemistry, history, and math
D. Biology, history, and math
2. Assuming that only two of each student’s four statements are true, which courses is Brittany taking?
A. Chemistry, biology, and history
B. Chemistry, biology, and math
C. Chemistry, history, and math
D. Biology, history, and math
3. Assuming that only two of each student’s four statements are true, which courses is Cheri taking?
A. Chemistry, biology, and history
B. Chemistry, biology, and math
C. Chemistry, history, and math
D. Biology, history, and math
4. Which two of Alice’s four statements are true?
A. There is only one subject that we are all taking; I am the only one of us who is taking math.
B. I am the only one of us taking math; the same three classes are not taken by any two of us.
C. There is only one subject we all take; the same three classes aren’t taken by any two of us.
D. No two of us take the same three classes; Cheri is wrong that Brittany and I take chemistry.
5. Which two of Brittany’s four statements are true?
A. Alice is the only one taking history; Cheri and I take the same classes.
B. Cheri and I take the same classes; all of us have a biology class.
C. All of us have a biology class; there are two of us taking biology and history.
D. Alice is the only one taking history; all of us have a biology class.
5. Which two of Cheri’s four statements are true?
A. All of us have a math class; Brittany is in a history course.
B. Brittany is in a history course; Alice has one class I don’t have.
C. All of us have a math class; Alice and Brittany both take chemistry.
D. Alice has one class I don’t have; Alice and Brittany both take chemistry.
Answer this question based on the following information:
Huey, Dewey, and Louie are playing paintball. When any one of them is marked with paint, he is out of that round of the game. Whichever one of them is left unmarked wins that round. Huey hits hit target 1/3 of the time. Dewey hits his target 2/3 of the time. Louie hits his target all of the time. Huey gets the first shot. Dewey gets the second chance, assuming that he has not been hit; and Louie gets to fire third, also assuming that he has not been hit. Any remaining players continue to fire in the same order until only one player remains.
6. Where should Huey aim first to give him the best chance of winning?
A. He should fire at Dewey first.
B. He should fire at Louie first.
C. He should fire at the ground first.
D. He should fire at himself first.
Answer the following questions based on the information below:
There is a jungle on an island cut off from the rest of the world. The jungle contains tigers and gazelles. Assume the following conditions: These tigers are super-intelligent, like human geniuses, and they have perfect logical reasoning. The tigers naturally want to eat gazelles. However, if a tiger eats a gazelle, the tiger itself is automatically transformed into a gazelle and can then be eaten by other tigers. Tigers do not want to be eaten. Assume further that one tiger always reaches the gazelles first. Also assume that a gazelle in this jungle cannot escape a tiger if the tiger intends to eat it.
7. If there is one gazelle and one tiger in the jungle, what will happen?
A. It is impossible to tell with the information given.
B. There is a 50/50 chance the tiger will eat the gazelle.
C. It is 100% certain that the tiger will eat the gazelle.
D. It is 100% certain the tiger will not eat the gazelle.
8. If there is one gazelle and two tigers on the island, what will occur?
A. It is impossible to tell based on the facts provided.
B. The gazelle will definitely get eaten by one tiger.
C. The odds are 50/50 that a tiger will eat the gazelle.
D. The gazelle will not be eaten by either of the tigers.
9. If there is one gazelle in the jungle and three tigers, what would be the outcome?
A. The gazelle is sure to be eaten by one of the tigers.
B. The gazelle will not be eaten by any of these tigers.
C. There is a 1 in 3 chance one tiger will eat the gazelle.
D. There is no way of predicting from this information.
10. Based on the information given, what general rule can be derived?
A. If there is any odd number of tigers, the gazelle is safe.
B. If there is any even number of tigers, the gazelle is safe.
C. A tiger will always eat the gazelle regardless of numbers.
D. No tiger will eat the gazelle, to avoid being transformed.
Answers – Logical Reasoning
1. A: Alice is taking chemistry, biology, and history. Alice’s statement is true that there is only one subject they all take, which is biology. Her statement is also true that no two students are taking the same three classes. Alice is not taking math, so her statement that she is the only one taking math is false, and all choices including math (B, C, and D) are incorrect.
2. B: Brittany is taking chemistry, biology, and math. Her statement that only Alice takes history is false: Cheri also takes history. Her statement that she and Cheri take the same classes is also false: they only take biology and math in common. Her statement that all of them take biology is true. Her statement that two of them both take biology and history is also true: Alice and Cheri both take biology and history.
3. D: Cheri is taking biology, history, and math. Cheri’s statement that all of them take math is false, as only Brittany and Cheri take math. Cheri’s statement that Brittany takes history is also false; Brittany takes chemistry, biology, and math. Cheri’s statement that Alice has one class she doesn’t have is true: Alice takes chemistry and Cheri does not. Her statement that Alice and Brittany both take chemistry is also true.
4. C: Alice’s statement is true that the three of them only take one class in common, which is biology; and it is also true that no two students are taking the same three courses. While it is true that there is only one subject they all take, it is not true that Alice is the only one taking math (A, B): Alice is not taking math. Alice’s statement that Cheri is wrong about Alice and Brittany both taking chemistry (D) is not true: Alice and Brittany both take chemistry and biology.
5. D: Cheri’s statement that Alice has one class she doesn’t have is true: Alice takes math but Cheri does not. It is also true that both Alice and Brittany are taking chemistry (as well as biology). It is not true that they all take math (A, C): only Brittany and Cheri take math; Alice does not. It is not true that Brittany takes history (B): she takes chemistry, biology, and math. Since only one of the two statements in B is true, this choice is incorrect. Only the second statement (Alice and Brittany take chemistry) is true in C; the first statement is false.
6. C: Huey should aim at the ground: he should not try to hit Dewey or Louie. Dewey will then aim at Louie. If he hits, Huey is 1-on-1 with Dewey, getting to fire the first shot (Huey’s odds >33.3%). If Louie is not hit and gets to fire, he will fire at Dewey, since Dewey is a better shot. This leaves Huey 1-on-1 with Louie, but still getting to fire the first shot (Huey’s odds =33.3%). If Huey were to aim at Dewey and hit, he would be guaranteed to lose since he would be the only target left for Louie, who never misses (Huey’s odds =0%). If Huey were to aim at Louie and hit, he would be left 1-on-1 with Dewey, but with Dewey firing the first shot (Huey’s odds <33.3%). Both of these outcomes offer Huey poorer odds than simply allowing Dewey and Louie to fire at each other first. 7. C: With one tiger and one gazelle, the tiger will always eat the gazelle because even though this transforms the tiger into a gazelle, the animal is safe as there are no other tigers in the jungle to eat him. It is possible to determine this with the information given, so A is incorrect. There is not a 50/50 chance (B) but a 100% certainty the one tiger will eat the gazelle. Therefore D is incorrect.
8. D: If there are two tigers and one gazelle, the gazelle will not be eaten. If one of the tigers were to eat the gazelle, he would be transformed into a gazelle, himself. Having eaten the original gazelle, he then would be the only gazelle, and the remaining tiger would be the only tiger and would eat him. As a result, both tigers will refrain from eating the gazelle to avoid being eaten themselves. It is not impossible to tell this based on the facts provided (A). The gazelle will not be eaten (B), and the chances of this are 100%, not 50/50 (C).
9. A: The gazelle is sure to be eaten by one of the tigers if there are three tigers. Any one of these tigers knows that if he eats the only gazelle, he will become the only gazelle himself, and there will be two other tigers. The former tiger that has become a gazelle is now safe, because with two tigers, neither one will eat him: they know that if one of them eats the gazelle, he will become a gazelle and there will be one tiger left that will eat him. Since A is correct, B, its opposite, is incorrect. There is not a 1 in 3 chance one tiger will eat the gazelle (C) but a 100% certainty. It is not true that there is no way of predicting this from the information given (D).
10. B: The general rule that can be derived from the information given is that as long as there is an even number of tigers, the gazelle is safe. The tigers know that with one gazelle and an even number of tigers, if a tiger eats a gazelle, he becomes the only gazelle, leaving an odd number of tigers. Then a tiger will eat the gazelle to restore the even number. Since B is true, A is false. It is not true that a tiger will always eat the gazelle regardless of numbers (C): the tigers logically reason that the one gazelle—including a tiger transformed into a gazelle—is safe with an even number of tigers and will not become vulnerable again by making the number odd. It is also not true that no tiger will ever eat the gazelle (D) to avoid being transformed: a tiger transformed into a gazelle is still safe from being eaten as long as there is an even number of tigers.