Problem 8 · 2006 AMC 8
Easy
Fractions, Decimals & Percents
two-way-table
The table shows some of the results of a survey by radio station KACL. What percentage of the males surveyed listen to the station? (Total surveyed: 200. Females: 96. Females who listen: 58. Males who don't listen: 26. Total listeners: 136. Total non-listeners: 64.)
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Answer: E — 75%.
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Hint 1 of 2
A two-way table is built on the rule that rows and columns must add to their totals. Find a cell you CAN fill (males total), then chase the rest.
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Hint 2 of 2
You only need the male row: total males, then split into listen/don't-listen. Ignore the female numbers once you have the male total.
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Approach: complete the male row, then take the percentage
- Total males = total surveyed − total females = 200 − 96 = 104.
- Males who listen = males total − males who don't = 104 − 26 = 78.
- Percentage of males who listen = 78 ÷ 104 = 75%.
- Shortcut worth seeing: instead of finding 78, note 26 out of 104 is exactly ¼ (since 26 × 4 = 104), so the non-listeners are 25% and the listeners are 100% − 25% = 75%. Spotting the clean fraction beats the division.
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