1993 AMC 8 Problem 13

Attempt Problem 13 of the 1993 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1993 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

13.

The word “HELP” in block letters is painted as a shaded region with strokes 11 unit wide on a 55 by 1515 rectangular sign. Each letter is 33 units wide with a 11-unit gap between letters, as shown. The area of the unshaded portion of the sign, in square units, is
3030
3232
3434
3636
3838
Answer: D
Concepts:area decomposition
Small hint:
The whole sign is 5×15=755 \times 15 = 75 square units
Big hint:
Count the shaded unit squares making up each letter, then subtract the total from 7575
Solution:
The full sign has area 5×15=755 \times 15 = 75 square units. Counting the shaded unit squares in each letter gives H=11,H = 11, E=11,E = 11, L=7,L = 7, and P=10,P = 10, for a shaded total of 11+11+7+10=39.11 + 11 + 7 + 10 = 39.
The unshaded area is 75−39=36.75 - 39 = 36.
Thus, the correct answer is D .
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