Tag: math & puzzles

Questions Related to math & puzzles

Each problem consists of three statements. Based on the first two statements, the third statement may be true, false, or uncertain. Tanya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true, the third statement is

  1. true

  2. false

  3. uncertain

  4. none


Correct Option: B
Explanation:

To solve this question, the user must analyze the given statements to determine the relationship between Tanya, Eric, and Cliff's ages.

Let's go through each statement one by one:

  1. Tanya is older than Eric. This statement implies that Tanya's age is greater than Eric's age.

  2. Cliff is older than Tanya. This statement suggests that Cliff's age is greater than Tanya's age.

  3. Eric is older than Cliff. This statement is contradictory to the first two statements. If Tanya is older than Eric, and Cliff is older than Tanya, it is impossible for Eric to be older than Cliff. Therefore, statement 3 is false.

Option A is incorrect because the third statement is false.

Option B is correct because the third statement is false.

Option C is incorrect because the third statement is not uncertain.

Option D is incorrect because the answer is option B, which is not "none."

Therefore, the answer is: B. false.

All the trees in the park are flowering trees. Some of the trees in the park are dogwoods. All dogwoods in the park are flowering trees. If the first two statements are true, the third statement is

  1. true

  2. false

  3. uncertain

  4. none


Correct Option: A

AI Explanation

To answer this question, we need to analyze the given statements and determine if the third statement is true, false, uncertain, or none of the above.

Let's go through each statement:

  1. All the trees in the park are flowering trees. This statement means that every tree in the park is a flowering tree. It indicates that there are no trees in the park that are not flowering trees.

  2. Some of the trees in the park are dogwoods. This statement means that there are at least a few trees in the park that are dogwoods. However, it does not provide information about whether all dogwoods are present in the park or if there are any dogwoods that are not in the park.

  3. All dogwoods in the park are flowering trees. This statement implies that every dogwood in the park is a flowering tree. It further suggests that there are no dogwoods in the park that are not flowering trees.

Based on the first two statements, we can conclude that all the trees in the park are flowering trees, and some of them are dogwoods. Since all dogwoods in the park are flowering trees, it is logical to conclude that the third statement is true.

Therefore, the correct answer is A) true.

Mara runs faster than Gail. Lily runs faster than Mara. Gail runs faster than Lily. If the first two statements are true, the third statement is

  1. true

  2. false

  3. uncertain

  4. none


Correct Option: B

AI Explanation

To answer this question, we need to analyze the statements given and determine their logical consistency.

Statement 1: Mara runs faster than Gail. Statement 2: Lily runs faster than Mara. Statement 3: Gail runs faster than Lily.

Let's analyze these statements one by one:

Statement 1: Mara runs faster than Gail. This statement is clear and consistent. We can assume it to be true.

Statement 2: Lily runs faster than Mara. This statement contradicts the first statement. If Mara runs faster than Gail and Lily runs faster than Mara, it is not possible for Gail to run faster than Lily. Therefore, this statement is false.

Statement 3: Gail runs faster than Lily. This statement contradicts the second statement. Since the second statement is false, we cannot determine the truth value of the third statement based on the given information.

Therefore, the correct answer is B. false.

Apartments in the Riverdale Manor cost less than apartments in The Gaslight Commons. Apartments in the Livingston Gate cost more than apartments in the The Gaslight Commons. Of the three apartment buildings, the Livingston Gate costs the most. If the first two statements are true, the third statement is

  1. true

  2. false

  3. uncertain

  4. none


Correct Option: A
Explanation:

To solve this question, the user needs to understand the relationship between the prices of apartments in the three buildings mentioned.

The first statement says that the apartments in Riverdale Manor cost less than the apartments in The Gaslight Commons. This means that the price of apartments in The Gaslight Commons is greater than the price of apartments in Riverdale Manor.

The second statement says that the apartments in Livingston Gate cost more than apartments in The Gaslight Commons. This means that the price of apartments in Livingston Gate is greater than the price of apartments in The Gaslight Commons.

The third statement says that Livingston Gate costs the most out of the three apartment buildings mentioned. Since we know that the price of apartments in The Gaslight Commons is greater than the price of apartments in Riverdale Manor, and the price of apartments in Livingston Gate is greater than the price of apartments in The Gaslight Commons, it follows that the price of apartments in Livingston Gate is the greatest of the three.

Therefore, the answer is:

The Answer is: A. true