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
- The following observation is made about the scores obtained by 100 students in an exam:
'For each student, there exists another student in the class such that their scores are at most ten marks away.'
If the above statement is false, which one of the following statements is necessarily true? - 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’? Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules:
- Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON.
- Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
- The state of any bulb not meeting the conditions above is left unchanged.
The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.
The number of bulbs which are ON at the end of Step 8 is ______
- 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:
