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port authority of new york and new jersey - RTA

📅 May 11, 2026 👤 scraface

May 11, 2026

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📌 So $k = 7m + 2$. Then $x = 60k = 60(7m + 2) = 420m + 120$. We seek the smallest three-digit such $x$:

📌 x = 420m + 120 \geq 100 \Rightarrow m \geq 0

📌 Try $m = 0$: $x = 120$ (valid, three-digit). Check $120 \mod 7 = 1$?

📌 \div 7 = 17 \text{ remainder } 1 \Rightarrow \text{Yes}

📌 Thus, the smallest such number is $\boxed{120}$.

📌 Question: What is the largest integer that must divide the product of any four consecutive odd integers?

📌 Solution: Let the four consecutive odd integers be $n, n+2, n+4, n+6$, where $n$ is odd. Their product is:

📌 P = n(n+2)(n+4)(n+6)

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