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

Question

Prepp Team · Accepted Answer

Car Collection Logic Puzzle Analysis

The problem involves determining the number of cars owned by S based on three statements, given that only one statement is true.

Let $n$ represent the number of cars S owns.

The statements can be represented mathematically:

P states: $n \ge 3$
Q states: $n < 3$
R states: $n \ge 1$

We are told exactly one of these statements is true.

Evaluating Possible Number of Cars

We test different values for $n$ to see when exactly one statement holds true:

Case 1: $n=0$
- P ($0 \ge 3$): False
- Q ($0 < 3$): True
- R ($0 \ge 1$): False
Result: Only Q is true. This matches the condition.
Case 2: $n=1$
- P ($1 \ge 3$): False
- Q ($1 < 3$): True
- R ($1 \ge 1$): True
Result: Q and R are true. This violates the condition.
Case 3: $n=2$
- P ($2 \ge 3$): False
- Q ($2 < 3$): True
- R ($2 \ge 1$): True
Result: Q and R are true. This violates the condition.
Case 4: $n \ge 3$
- P ($n \ge 3$): True
- Q ($n < 3$): False
- R ($n \ge 1$): True (since $n \ge 3$ implies $n \ge 1$)
Result: P and R are true. This violates the condition.