Introduction / Context:
This reasoning question involves recognizing a simple digit pattern. The task is to select the number that does not share the same property regarding distinct digits as the others. Odd one out problems using digit repetition are common because they are easy to understand yet still require careful observation.
Given Data / Assumptions:
- The numbers given are 532, 413, 111 and 541.
- We inspect the digits of each number individually.
- The suspected pattern is based on whether digits repeat within a number.
Concept / Approach:The idea is to see whether all digits in a number are distinct or whether some digit is repeated. If three of the numbers have all unique digits, and one number has repeating digits, then the number with repeating digits is the odd one out. This is a direct and intuitive property that does not require any heavy arithmetic.
Step-by-Step Solution:Step 1: For 532, the digits are 5, 3 and 2. All three digits are different.Step 2: For 413, the digits are 4, 1 and 3. Again, all three digits are distinct.Step 3: For 541, the digits are 5, 4 and 1. All three digits are distinct here as well.Step 4: For 111, the digits are 1, 1 and 1. All three digits are the same, so there is complete repetition.Step 5: Since 532, 413 and 541 each have distinct digits, while 111 consists of the same digit repeated three times, 111 clearly stands out as the odd one out.Verification / Alternative check:An alternative method is to count the number of distinct digits in each number. The distinct digit count is 3 for 532, 3 for 413, 3 for 541 and only 1 for 111. Therefore, 111 is the only number with fewer than 3 distinct digits, confirming it as the unique case in the group.
Why Other Options Are Wrong:532 is not the odd one out because its digits are all different and follow the same pattern as 413 and 541.413 is also not unique, since it features three distinct digits just like 532 and 541.541 again has three different digits and therefore belongs together with 532 and 413.
Common Pitfalls:Sometimes candidates look for complex arithmetic properties such as divisibility or prime status and miss the simple digit repetition pattern. Another pitfall is to overlook that all digits in 111 are the same, which is visually obvious but can be ignored when solving too quickly. It is always helpful to first check for simple and visible properties such as repetition, parity and digit count before attempting more complex rules.
Final Answer:The only number that has repeating digits instead of distinct digits is
111, so 111 is the odd one out.
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