True/False statements logic puzzle for candidates
Question
Consider the following statements in respect of five candidates P, Q, R, S and T. Two statements are true and one statement is false. True Statement: One of P and Q was selected for the job. False Statement: At least one of R and S was selected for the job. True Statement: At most two of R, S and T were selected for the job. Which of the following conclusions can be drawn?
Options
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Explanation
Analyze the conditions by decoding the specified true/false values systematically :
Step 1: The statement "At least one of R and S was selected" is given as FALSE[cite: 4426, 4482]. Negating a false existential statement means that neither R nor S was selected for the job (R = 0, S = 0). This immediately invalidates Conclusion 2 ("S was selected") [cite: 4431, 4510].
Step 2: Evaluate the true statements with this knowledge:
Total possible selections = 1 (from P/Q) + 0 (R) + 0 (S) + T (0 or 1) = maximum of 2 people. This completely disproves Conclusion 1 ("At least four were selected")[cite: 4429, 4507]. Neither conclusion follows[cite: 4436, 4534].
Answer: (d).
Question details
Year
2023
Paper
CSAT
Question
Q77
Section
Logical & Analytical Reasoning
Sub-topic
Logical Puzzles
Type
Inequality logic
Difficulty
Hard
Source hint
Logical deduction
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