Question

A rectangular floor that is $10$ feet wide and $17$ feet long is tiled with $170$ one-foot square tiles. A bug walks from one corner to the opposite corner in a straight line. Including the first and the last tile, how many tiles does the bug visit?

$17$

$25$

$26$

$27$

$28$

Answer: C

Concepts:greatest common divisor counting intersections

Difficulty rating: 1240

Solution:

Note that every time the bug crosses a vertical or horizontal line, the bug visits one new tile.

This means that the number of tiles the bug visits is $1$ (the first tile) plus the number of lines it crosses.

The bug never walks over a corner since $10$ and $17$ are relatively prime, so we don't have to worry about that.

The bug crosses $16$ horizontal lines and $9$ vertical lines for a total of $1 + 16 + 9 = 26$ tiles.

Thus, C is the correct answer.

2019 AMC 10A Problem 10

Answer: C

Difficulty rating: 1240

Solution:

Problem 10 in Other Years