What proportion of integers ranging from 1 to 70 yield squares terminating in the digit 1?
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Answer: C. 20
Explanation
Integers whose squares terminate in the digit one must end in either one or nine. Every decade from one to seventy contains two numbers ending in one or nine. Multiplying the two numbers per decade across seven decades yields twenty total integers. The last digit of a square number depends entirely on the last digit of its base root. Modular arithmetic principles govern the ending digits of squared integer values. Systematic counting across defined numerical ranges ensures complete and accurate totals.
Number theory applications include cryptography algorithms and pattern analysis in mathematics. Computer science algorithms use modular arithmetic properties for hash table indexing. Mathematical puzzles often test an understanding of square root and ending digit patterns. Option A severely underestimates the count of qualifying integers in the range. Option B counts only one qualifying number per decade instead of the required two. Option D overestimates the count by including incorrect base number endings.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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