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Home » 4x = 11,000 → x = 2750. - DNSFLEX

4x = 11,000 → x = 2750. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 An ornithologist uses GPS tracking to study a flock of geese whose flight paths form a repeating cycle every \( k \) days. She observes that a particular behavioral pattern occurs every \( k \) days, where \( k \) is the smallest two-digit number such that \( k \) is divisible by the sum of its digits and leaves a remainder of 2 when divided by 7. What is \( k \)?

📌 We seek the smallest two-digit number \( k \) such that:

📌 \( k \equiv 2 \pmod{7} \),

📌 \( k \) is divisible by the sum of its digits.

📌 Let \( k = 10a + b \), where \( a \in \{1,2,\dots,9\} \), \( b \in \{0,1,\dots,9\} \), so sum of digits is \( a + b \).

📌 We check two-digit numbers \( k \equiv 2 \pmod{7} \): they are:

📌 k = 16, 23, 30, 37, 44, 51, 58, 65, 72, 79, 86, 93

📌 Now test each for divisibility by digit sum:

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