One of four suspects A, B, C and D has committed a crime. A and D are always truthful, and B and C are always untruthful. C and D are identical twins and the interrogator does not know who is who. If A says, "D is innocent", B says, "A is guilty" and among C and D one says, "A is innocent" and the other says, "B is guilty", then which of the following is FALSE?
This problem involves analyzing statements made by suspects with known truth-telling or lying tendencies to determine their guilt or innocence and identify which statement is false. We have four suspects: A, B, C, and D. A and D always tell the truth, while B and C always lie. C and D are identical twins, making it tricky to distinguish them initially.
Suspect Analysis and Statement Evaluation
Let's break down the information given:
- A: Truthful
- B: Untruthful (Liar)
- C: Untruthful (Liar)
- D: Truthful
C and D are twins, one truthful (D), one untruthful (C).
Evaluating Individual Statements
- A says, "D is innocent": Since A is always truthful, this statement is true. Therefore, D is innocent.
- B says, "A is guilty": Since B is always untruthful, this statement is false. The opposite must be true. Therefore, A is not guilty (A is innocent). This aligns with A being truthful, as a truthful person is unlikely to be the criminal.
- Among C and D, one says, "A is innocent" and the other says, "B is guilty":
- We know D is truthful and C is untruthful.
- We know "A is innocent" is a true statement (from evaluating A's and B's statements).
- Since D is truthful, D must be the one who says the true statement. Thus, D says, "A is innocent".
- This leaves C, the untruthful twin, to say the other statement: C says, "B is guilty".
- Since C is untruthful, C's statement "B is guilty" must be false. The opposite is true: B is not guilty (B is innocent).
Summary of Deductions
Based on the statements and the nature of the suspects, we can deduce the following:
- A is truthful and innocent.
- B is untruthful and innocent.
- D is truthful and innocent.
- C is untruthful. C said "B is guilty" which is a lie. If B is innocent (which we deduced), then C lied. This fits C's nature. Since only one suspect committed the crime, and A, B, and D are innocent, C must be the guilty one.
Let's summarise who is truthful/untruthful, who is innocent/guilty, and what each person said:
| Suspect | Truthful/Untruthful | Innocent/Guilty | Statement Made | Truth of Statement |
|---|---|---|---|---|
| A | Truthful | Innocent | "D is innocent" | True |
| B | Untruthful | Innocent | "A is guilty" | False |
| C (Twin) | Untruthful | Guilty | "B is guilty" | False |
| D (Twin) | Truthful | Innocent | "A is innocent" | True |
Evaluating the Options
We need to find the statement among the options that is FALSE based on our deductions.
- D said "A is innocent": From our analysis, D (the truthful twin) said "A is innocent". This statement is TRUE.
- D is innocent: From A's statement and our deductions, D is indeed innocent. This statement is TRUE.
- B is innocent: From C's lie ("B is guilty"), we deduced that B is innocent. This statement is TRUE.
- C is innocent: From our deductions, C is the untruthful twin who lied about B, and is the only remaining suspect who could have committed the crime. C is guilty, not innocent. This statement is FALSE.
Therefore, the statement that is FALSE is "C is innocent".
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A mass is attached to a spring that hangs vertically. The extension produced in the spring is 6 cm on Earth. The acceleration due to gravity on the surface of the Moon is one-sixth of its value on the surface of the Earth. The extension of the spring on the Moon would be:
Directions: Each item in this section consists of a sentence with an underlined word followed by four words (a), (b), (c), and (d). Select the option that is opposite in meaning to the underlined word and mark your response in your Answer Sheet accordingly.
The deluge affected the population.The major source of vitamins and minerals for vegetarians is
Which of the following statements about the Deccan Riots Commission is/are correct?
1. The Commission did not hold enquiries in the districts which were not affected.
2. The Commission did record the statements of ryots, sahukars and eye-witnesses.
Select the correct answer using the code given below:
