Problem 15 · 2018 Math Kangaroo
Hard
Fractions, Decimals & Percents
percent-multiplier
At a humanistic university you can study languages, history or philosophy. Some students study exactly one language (nobody studies several at once). Among those language students, 35% study English. Among all students of the university, 13% study a language other than English. What percentage of all students study a language?
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Answer: B — 20 %
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Hint 1 of 2
If 35% of language students study English, then 65% study a non-English language.
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Hint 2 of 2
That 65% of the language group equals 13% of all students.
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Approach: the non-English language students link the two percentages
- Among language students, 35% study English, so 65% study another language.
- Those non-English language students are 13% of all students, so 65% of the language group = 13% of everyone.
- Thus the language group is \(13\% \div 0.65 = \) 20% of all students.
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