What is the mean of the two-digit numbers that remain unchanged when their digits are reversed__________?
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Answer: C. 55
Explanation
Two digit numbers remaining unchanged when reversed must have identical tens and units digits. The complete set of these palindromic numbers ranges from eleven through ninety nine at intervals of eleven. The arithmetic mean of this evenly spaced symmetric sequence of numbers is its exact middle value. Palindromic numbers read the same forward and backward in standard positional base ten notation. An arithmetic sequence with a constant common difference has a mean equal to its median value. Two digit numbers are bounded strictly between ten and ninety nine inclusive.
Number theory explores palindromic patterns and properties within various mathematical base systems. Cryptographic algorithms sometimes utilize symmetric digit arrangements for digital signature verification. Recreational mathematics frequently features number reversal puzzles to engage students in logic. Option A represents only the lower third value within the sequence of palindromic numbers. Option B represents a single number in the sequence rather than the calculated mean value. Option D represents a higher value located near the upper end of the number set.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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