1992 AMC 8 Problem 21

Below is the professionally curated solution for Problem 21 of the 1992 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1992 AMC 8 solutions, or check the answer key.

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Concepts:data and graph interpretationpercentage

Difficulty rating: 1130

21.

Northside's Drum and Bugle Corps raised money for a trip. The drummers and bugle players kept separate sales records. According to the double bar graph of monthly sales below, in what month did one group's sales exceed the other's by the greatest percent?

Jan

Feb

Mar

Apr

May

Solution:

Reading the graph gives (drums, bugles): January (7,9),(7, 9), February (5,3),(5, 3), March (9,6),(9, 6), April (9,12),(9, 12), and May (8,10).(8, 10).

The percent excess of the larger over the smaller is 2729%\tfrac{2}{7} \approx 29\% in January, 2367%\tfrac{2}{3} \approx 67\% in February, 36=50%\tfrac{3}{6} = 50\% in March, 3933%\tfrac{3}{9} \approx 33\% in April, and 28=25%\tfrac{2}{8} = 25\% in May. The greatest is February, where 55 exceeds 33 by about 67%.67\%.

Thus, the correct answer is B .

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