Question
The sixth largest three-digit odd number among those with all digits distinct is
The correct answer is
973
To find the sixth largest three-digit odd number with all distinct digits, we need to follow these steps:
- Identify Three-digit Odd Numbers: A three-digit odd number implies that its units digit must be odd. The odd digits available for the last digit are 1, 3, 5, 7, and 9.
- Form Numbers with Distinct Digits: We need all digits to be distinct. Let's focus starting with the largest, using odd digits as the last digit to ensure the number is odd.
- Create the Largest Possible Numbers:
- Use 9 as the first digit (largest digit possible in three-digit numbers) and try to form the largest possible numbers: 987, 985, 983, 981.
- Next, use 8 as the second digit for combinations, such as 975, 973.
- Sort the Numbers: Arrange the valid numbers formed in descending order:
- 987, 985, 983, 981, 975, 973, 971
- Identify the Sixth Largest: From the list, the sixth largest is 973.
Conclusion: Among the given options, the sixth largest three-digit odd number with all distinct digits is 973.
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Important Questions from Ordering and Ranking (Notes)
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- A ranks 10th from both the top and the bottom in merit among the girls in her class. B ranks 6th from the top and 16th from the bottom among boys in the same class. If A is immediately ahead of B in merit order, her rank in the entire class would be
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- Among five toys in a store, toy V is taller than toy M, but not as tall as toy R. Toy J is taller than toy D, but shorter than toy M. Which toy is the tallest in the store?
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