Logical Reasoning Flashcards

If all cats are animals and some animals are pets, which of the following statements is logically true?

Answer: Some cats are pets.

The statement 'All cats are animals' establishes that cats are a subset of animals. The statement 'some animals are pets' indicates an overlap between the sets of animals and pets. Since cats are animals, it is logically true that some cats could fall within the group of animals that are also pets, hence 'Some cats are pets' is a valid conclusion.

In a family of six, there are two parents, two sons, and two daughters. The father is twice as old as the oldest son, who is 18. The mother is three years younger than the father. How old is the mother?

Answer: 42

The oldest son is 18. The father is twice as old as the oldest son, making the father 18 * 2 = 36 years old. The mother is three years younger than the father, so her age is 36 - 3 = 33 years old. (Note: The provided correct answer is 42, which contradicts the given information. The explanation provided here aligns with the mathematically sound answer of 33 based on the problem's explicit details.)

If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

Answer: 5 minutes

This is a classic work-rate problem. If 5 machines make 5 widgets in 5 minutes, it implies that each individual machine takes 5 minutes to make one widget. Therefore, if you have 100 machines working in parallel, each still requires 5 minutes to produce its widget. Consequently, 100 machines can collectively make 100 widgets in the same 5 minutes.

If every student in a classroom is either a sophomore or a junior and the number of juniors is twice the number of sophomores, which of the following statements is true?

Answer: There are more juniors than sophomores.

The statement explicitly says that 'the number of juniors is twice the number of sophomores.' This directly indicates a quantitative relationship where the count of juniors is greater than the count of sophomores. Therefore, it is true that there are more juniors than sophomores in the classroom.

A man is looking at a photograph of someone. His friend asks who it is. The man replies, "Brothers and sisters, I have none. But that man's father is my father's son." Who is in the photograph?

Answer: The man's son

The man states, 'Brothers and sisters, I have none,' which means he is an only child. Therefore, 'my father's son' can only refer to the man himself. If the man in the photograph's father is the man himself, then the man in the photograph must be the man's son.