1992 AMC 8 Problem 21

Attempt Problem 21 of the 1992 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 1992 AMC 8 solutions, or check the answer key.

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

21.

Northside’s Drum and Bugle Corps raised money for a trip. The drummers and bugle players kept separate sales records. In each pair on the graph, the open bar represents drums and the shaded bar represents bugles. 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
Answer: B
Concepts:data and graph interpretationpercentage
Small hint:
For each month, read off the two bar heights and find the gap between them
Big hint:
Divide the difference by the smaller value to find the percent by which the larger exceeds it; compare this ratio across the months
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 27≈29%\tfrac{2}{7} \approx 29\% in January, 23≈67%\tfrac{2}{3} \approx 67\% in February, 36=50%\tfrac{3}{6} = 50\% in March, 39≈33%\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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