P, Q, and R talk about S’s car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least one car. Only one of P, Q and R is right. The number of cars owned by S is
0
Car Collection Logic Puzzle Explained
This problem is a classic example of a logical reasoning puzzle where we need to deduce the correct number of cars owned by S based on conflicting statements from three individuals, P, Q, and R, with the crucial condition that only one of them is telling the truth.
Understanding the Statements
Let's first break down each person's statement about S's car collection:
- P's statement: "S has at least 3 cars." This can be mathematically represented as $\text{S} \geq 3$.
- Q's statement: "S has less than 3 cars." This can be mathematically represented as $\text{S} < 3$.
- R's statement: "To his knowledge, S has at least one car." This can be mathematically represented as $\text{S} \geq 1$.
The core condition given is that only one of P, Q, and R is right (i.e., their statement is true).
Analyzing Possible Scenarios for S's Cars
To find the correct number of cars S owns, we will test different possible numbers of cars and see which scenario satisfies the condition that exactly one statement is true. We'll evaluate each statement (True or False) for various values of S.
| Number of Cars (S) | P's Statement ($\text{S} \geq 3$) | Q's Statement ($\text{S} < 3$) | R's Statement ($\text{S} \geq 1$) | Number of True Statements | Is Condition Met? (Exactly One True) |
|---|---|---|---|---|---|
| 0 | False | True | False | 1 | Yes |
| 1 | False | True | True | 2 | No |
| 2 | False | True | True | 2 | No |
| 3 | True | False | True | 2 | No |
| 4 (or any $\text{S} > 3$) | True | False | True | 2 | No |
Step-by-Step Evaluation
Let's examine each possible number of cars for S in detail:
- Case 1: S owns 0 cars
- P states $\text{S} \geq 3$: This is False, as $0$ is not greater than or equal to $3$.
- Q states $\text{S} < 3$: This is True, as $0$ is less than $3$.
- R states $\text{S} \geq 1$: This is False, as $0$ is not greater than or equal to $1$.
- In this case, only Q's statement is true. This satisfies the condition that "only one of P, Q and R is right."
- Case 2: S owns 1 car
- P states $\text{S} \geq 3$: This is False, as $1$ is not greater than or equal to $3$.
- Q states $\text{S} < 3$: This is True, as $1$ is less than $3$.
- R states $\text{S} \geq 1$: This is True, as $1$ is greater than or equal to $1$.
- In this case, both Q and R's statements are true. This violates the condition that "only one of P, Q and R is right."
- Case 3: S owns 2 cars
- P states $\text{S} \geq 3$: This is False, as $2$ is not greater than or equal to $3$.
- Q states $\text{S} < 3$: This is True, as $2$ is less than $3$.
- R states $\text{S} \geq 1$: This is True, as $2$ is greater than or equal to $1$.
- Similar to the previous case, both Q and R's statements are true. This violates the condition.
- Case 4: S owns 3 cars
- P states $\text{S} \geq 3$: This is True, as $3$ is greater than or equal to $3$.
- Q states $\text{S} < 3$: This is False, as $3$ is not less than $3$.
- R states $\text{S} \geq 1$: This is True, as $3$ is greater than or equal to $1$.
- Here, both P and R's statements are true. This again violates the condition.
- Case 5: S owns more than 3 cars (e.g., S = 4)
- P states $\text{S} \geq 3$: This is True, as $4$ is greater than or equal to $3$.
- Q states $\text{S} < 3$: This is False, as $4$ is not less than $3$.
- R states $\text{S} \geq 1$: This is True, as $4$ is greater than or equal to $1$.
- Again, both P and R's statements are true. This violates the condition.
Conclusion on S's Car Collection
Based on the detailed analysis of all possible scenarios, the only number of cars for S that satisfies the condition that "only one of P, Q, and R is right" is 0. In this specific situation, Q's statement ("S has less than 3 cars") is true, while P's and R's statements are false.
Therefore, the number of cars owned by S is 0.
Important Questions from Critical Reasoning
'Little knowledge is a dangerous thing' is a decision based on:
Which of the following is the assumption for the claim that 'Pleasure is desirable'?
Read the given statements carefully and answer the questions.
Fear of danger is more dangerous than danger itself. Risk is directly proportional= to danger
Which of the following are true according to the given statements?
A. Fear is worse than any fearful threat.
B. There is a trade-off between risk and danger.
C. There should be fear of danger.
D. There is no need to take risks to overcome any danger.
A question has been given in this question and a statement related to it. Read the passage carefully and review the statement based on it.
Amazon has acknowledged the data violation of user names and email ids of some users without giving details of its nature or scope. Although the company has not disclosed the total number of users affected by this violation, it has sent information to all affected users about the technical problem. And now this e-commerce major company is offering Gift Cards as compensation to customers who are victims of their data violation. This e-commerce company headquartered in Seattle is offering Gift Cards between $ 5 to $ 100 for users affected by some of their data violations.
A publication mentioning email communications between Amazon and a customer Paul Gagnon has reported that when he asked the customer service desk to ask the company how his information was leaked, then the company gave him a promotion of $ 100 Certificate offered. When Gagan got no response for the reason of this violation, he was offered $ 100 as an apology. After this violation, many affected users had filed a complaint with the service desk. Many people affected by this violation complained to the company, but none of them got so far. It is being speculated that Amazon Customer Service Supervisors have been instructed not to offer any comments or any kind of compensation to affected Amazon users.
Statement: The company has not told the fixed number of people affected by data violation. Select the most suitable option below.
A-statement is definitely true.
B-Query is probably true.
C-statement can not be determined.
D-statement is completely false.
A question has been given in this question and a statement related to it. Read the passage carefully and review the statement based on it.
Amazon has acknowledged the data violation of the user name and email id of some of its users, without giving details of its nature or scope. Although the company has not disclosed the total number of users affected by this violation, it has sent information to all affected users about the technical problem. And now this e-commerce major company is offering Gift Cards as compensation to customers who are victims of their data violation. This e-commerce company headquartered in Seattle is offering Gift Cards between $ 5 to $ 100 for users affected by some of their data violations.
A publication mentioning email communications between Amazon and a customer Paul Gagnon has reported that when he asked the customer service desk to ask the company how his information was leaked, then the company gave him a promotion of $ 100 Certificate offered. When Gagan got no response for the reason of this violation, he was offered $ 100 as an apology. After this violation, many affected users had filed a complaint with the service desk. Many people affected by this violation complained to the company, but none of them got so far. It is being speculated that Amazon Customer Service Supervisors have been instructed not to offer any comments or any kind of compensation to affected Amazon users.
Statement: Amazon has not instructed its supervisors to not provide any comments or offers of compensation to the affected users.
Select the most suitable option below.
A-statement is definitely true.
B-Query is probably true.
C-statement can not be determined.
D-statement is completely false.
