Analyzing the Statements

Let $N$ be the number of cars S owns.

• P's statement: $N \ge 3$.
• Q's statement: $N < 3$ (which means $N = 0, 1,$ or $2$).
• R's statement: $N \ge 1$.

We are given that only one of these statements is true.

Evaluating Scenarios

We test each person being the sole truth-teller:

Scenario 1: Only P is telling the truth.

• P is True: $N \ge 3$.
• Q is False: It is NOT true that $N < 3$. So, $N \ge 3$.
• R is False: It is NOT true that $N \ge 1$. So, $N < 1$ (i.e., $N = 0$).

This leads to a contradiction ($N \ge 3$ and $N = 0$). So, P cannot be the only one telling the truth.

Scenario 2: Only Q is telling the truth.

• Q is True: $N < 3$ (i.e., $N = 0, 1,$ or $2$).
• P is False: It is NOT true that $N \ge 3$. So, $N < 3$.
• R is False: It is NOT true that $N \ge 1$. So, $N < 1$ (i.e., $N = 0$).

If $N = 0$, then:

• P's statement ($N \ge 3$) is False.
• Q's statement ($N < 3$) is True.
• R's statement ($N \ge 1$) is False.

This perfectly fits the condition that only one person (Q) is telling the truth. Therefore, the number of cars must be 0.

Scenario 3: Only R is telling the truth.

• R is True: $N \ge 1$.
• P is False: It is NOT true that $N \ge 3$. So, $N < 3$.
• Q is False: It is NOT true that $N < 3$. So, $N \ge 3$.

This leads to a contradiction ($N < 3$ and $N \ge 3$). So, R cannot be the only one telling the truth.

Conclusion

The only consistent scenario is when Q is telling the truth, which implies that S owns 0 cars.