Question

Ronny uses a 5-digit key for a combination lock, where 5 digits need to be entered in a fixed sequence. While he remembers that the 5 digits are 9, 8, 7, 5, and 4, he has forgotten the sequence he uses. He also remembers that the sum of the first three digits is a multiple of 3, and so is the sum of the last three digits. Further, the sum of the last four digits is a multiple of 4.
Which of the following is DEFINITELY FALSE?

• A. 9 is the third digit of the key
• B. 8 is the second digit of the key
• C. 8 is the fourth digit of the key
• D. 4 is the fourth digit of the key
• E. 4 is the second digit of the key

Hint:

When dealing with such puzzles, carefully test each condition for all possible placements of the digits, ensuring that the sums meet the required multiples.

Answer 1

The Correct Option is C

Step 1: List the given digits.
The 5 digits are 9, 8, 7, 5, and 4, but their sequence is unknown.
Step 2: Analyze the conditions.
- The sum of the first three digits must be a multiple of 3. - The sum of the last three digits must be a multiple of 3. - The sum of the last four digits must be a multiple of 4.
Step 3: Check each option.
We know that: - The sum of the last four digits must be a multiple of 4. The sum of the four digits is \( 9 + 8 + 7 + 5 = 29 \), and we must check if this sum fits the condition. This doesn't work, so the combination where 8 is the fourth digit will be impossible.
Step 4: Conclusion.
The correct answer is (C) because having 8 as the fourth digit does not satisfy the conditions.