Sample Question 10:

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?

\(\textbf{(A) } 17 \qquad\textbf{(B) } 25 \qquad\textbf{(C) } 26 \qquad\textbf{(D) } 27 \qquad\textbf{(E) } 28\)

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Answer Keys

Question 10: C

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Solutions

Question 10
Step 1: Understand that the number of tiles the bug visits will be equal to 1 plus the number of times it crosses a horizontal or vertical line.

Step 2: Identify the number of horizontal lines the bug will cross, which is 16 in this case, because there are 17 tiles along the length, so the bug will have to move from one tile to another 16 times.

Step 3: Identify the number of vertical lines the bug will cross, which is 9 in this case, because there are 10 tiles along the width, so the bug will have to cross from one tile to another 9 times.

Step 4: Add the number of horizontal lines crossed, the number of vertical lines crossed, and 1 together to get the total number of tiles visited. So, the bug visits 16 (horizontal lines) + 9 (vertical lines) + 1 = 26 tiles in total.

Hence, the answer is \(\boxed{\textbf{(C) }26}\).