Question

If Samuel is telling the truth, which of the following statements is true?

• A. Chaudhary and Datta are telling the truth
• B. Nagraj fudged the accounts
• C. Chaudhary and Jose are telling the truth
• D. Shrinivas and Datta are telling the truth
• E. Nagraj fudged the account
• A. Nagraj, Ganeshan and Ejaz are all lying
• B. Datta fudged the accounts
• C. Shrinivas did not fudge the accounts
• D. Jose and Shrinivas are telling the truth
• J. Nagraj did not fudge the accounts

Answer 1

The Correct Option is A

Step 1: Recall Samuel’s condition.
Samuel says: “Exactly three suspects are telling the truth.” If Samuel is truthful, then exactly three statements (including Samuel’s) must be true. Hence, there are 3 truth-tellers and 6 liars.
Step 2: Eliminate Panda.
Panda says Samuel is lying. If Samuel is truthful, Panda must be lying.
Step 3: Case analysis.
Case I: Assume Shrinivas is telling the truth.
If Shrinivas is truthful, then Nagraj fudged the accounts. Jose, who supports Shrinivas, must also be truthful. That already gives Samuel, Shrinivas, and Jose as truth-tellers. But Datta’s statement (“Shrinivas did not fudge”) directly contradicts Shrinivas, meaning Datta is lying. However, Nagraj’s statement partly aligns and would add more truth-tellers, exceeding the limit of three. Contradiction. Therefore, this case is invalid.
Case II: Assume Datta is telling the truth.
If Datta is truthful, then “Shrinivas did not fudge” is correct, meaning Shrinivas is lying. Hence, Nagraj’s claim (“Datta is lying…”) is false. Ejaz’s claim is also false. Jose’s claim (“Shrinivas is telling the truth”) is false. Ganeshan’s statement is false. Panda is already lying. Therefore, the truth-tellers are: Samuel, Datta, and Chaudhary. This gives exactly three truth-tellers, which is valid.
Case III: Assume Datta is lying.
If Datta is lying, then Shrinivas’s status changes and may create more than three truth-tellers. In this scenario, multiple overlaps occur, leading to more than three truth-tellers. This contradicts Samuel’s condition. Therefore, invalid.
Step 4: Conclusion.
The only valid distribution of truth-tellers is Samuel, Datta, and Chaudhary. \[ \boxed{\text{Correct Answer: (A) Chaudhary and Datta are telling the truth}} \]

Answer 2

Step 1: Interpret Panda’s statement.
Panda says: “Samuel is lying.” If Panda is lying, then Samuel is truthful. Samuel’s claim is that exactly three suspects are telling the truth. Therefore, there must be exactly three truth-tellers.
Step 2: Fix the truth-tellers.
From Q38’s analysis, the consistent truth-tellers are: Samuel, Datta, and Chaudhary. Everyone else, including Panda, Shrinivas, Jose, Nagraj, Ejaz, and Ganeshan, must be lying.
Step 3: Evaluate each option.
- (A) Nagraj, Ganeshan, and Ejaz all lying → Matches the distribution, so it is possible. Valid.
- (B) Datta fudged the accounts → Chaudhary’s statement confirms this and Chaudhary is truthful. Valid.
- (C) Shrinivas did not fudge the accounts → Datta stated this, and Datta is truthful. Valid.
- (D) Jose and Shrinivas are telling the truth → Both are established as liars. This cannot be true. Invalid.
- (E) Nagraj did not fudge the accounts → Since Shrinivas’s claim was false, this is consistent. Valid.
Step 4: Conclusion.
The only option that cannot be true is (D) Jose and Shrinivas being truth-tellers. \[ \boxed{\text{Correct Answer: (D) Jose and Shrinivas are telling the truth}} \]