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.
Important Questions from Logical Deduction
- Consider the following two phonological rules:
Rule 1: Vowel Epenthesis of [ɪ] after sibilant-ending stems
Rule 2: Progressive Voicing Assimilation of the plural affix
Which ONE of the following rule ordering relations apply in the case of regular English pluralization as in ‘horse’ – ‘horses’? - Based only on the conversation below, identify the logically correct inference:
“Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine. Consider a five-digit number PQRST that has distinct digits P, Q, R, S and T, and satisfies the following conditions:
$P < Q$
$S > P > T$
$R < T$
If integers 1 through 5 are used to construct such a number, the value of P is:Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of these academicians are authors of some best-selling books.
Based only on the information provided above, which one of the following statements can be logically inferred with certainty?- The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:
P says "Q committed the crime.”
Q says "S committed the crime. "
R says"I did not do it."
S says "What Q said about me is false."
Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?
