1994 AMC 8 Problem 15

Below is the professionally curated solution for Problem 15 of the 1994 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1994 AMC 8 solutions, or check the answer key.

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Concepts:modular arithmetic pattern recognition

Difficulty rating: 910

15.

If this path is to continue in the same pattern, then which sequence of arrows goes from point $425$ to point $427?$

Solution:

The pattern repeats every $4$ points, so the arrows leaving a point depend only on its remainder upon division by $4.$

Because $425 = 4(106) + 1$ and $427 = 4(106) + 3,$ the path from $425$ to $427$ looks just like the path from point $1$ to point $3$ : from $1$ it goes up to $2,$ then right to $3.$

Thus, the correct answer is A .

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