Who is telling the truth — Aptitude Question
Who is telling the truth: A says 'B is lying', and B says 'C is lying', while C says 'both A and B are lying'. Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 150 seconds
Question
A says 'B is lying', and B says 'C is lying', while C says 'both A and B are lying'. Who is telling the truth?
Options
- A only
- B only
- C only
- A and C
Show the answer and the worked solution
Correct answer: B. B only
Worked solution
- Suppose A is truthful. Then B lies, so C's statement 'C is lying' being false means C is truthful. But C claims A and B both lie, contradicting A being truthful. ✗
- Suppose A is lying. Then B is truthful, so C is lying.
- Check C: C claims A and B both lie. A does lie but B does not, so C's claim is false — consistent with C lying. ✓
- The consistent assignment is A lying, B truthful, C lying, so B only tells the truth.
Answer: B only.
The idea
Assume each person truthful in turn and follow the consequences until a contradiction appears. Exactly one assignment should survive.
Shortcut. C's claim defeats itself: if A and B both lied, A's 'B is lying' would be true. So C lies, making B's 'C is lying' true, and A, who calls B a liar, lies.
Common trap. "A and C" — assuming A truthful, deducing that B lies and so C tells the truth, then stopping without checking C's claim that A lies.