Problem 16 · 2012 Math Kangaroo
Medium
Number Theory
careful-countingoff-by-one
How many natural numbers n are there for which \(n - 24\) and \(n + 24\) are two-digit numbers?
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Answer: A — 42
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Hint 1 of 2
Two-digit numbers run from 10 to 99.
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Hint 2 of 2
Turn both conditions into a range for n, then count the whole numbers in it.
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Approach: bound then count
- n − 24 ≥ 10 gives n ≥ 34; n + 24 ≤ 99 gives n ≤ 75.
- So n runs over the whole numbers 34 to 75.
- That is 75 − 34 + 1 = 42 values.
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