At the Zamenhof Language School, at least 70% of the students take English each year, at least 40% take German each year, and between 30% and 60% take Italian each year. Every student must take at least one of these three languages, and no student is allowed to take more than two languages in the same year. What is the possible percentage range for students taking both English and German in the same year?

(A) 0% to 70% (B) 0% to 100% (C) 10% to 70% (D) 10% to 100% (E) 40% to 70%

Question

Timothy Elliott

Mathematics

6 March, 21:27

At the Zamenhof Language School, at least 70% of the students take English each year, at least 40% take German each year, and between 30% and 60% take Italian each year. Every student must take at least one of these three languages, and no student is allowed to take more than two languages in the same year. What is the possible percentage range for students taking both English and German in the same year?

(A) 0% to 70% (B) 0% to 100% (C) 10% to 70% (D) 10% to 100% (E) 40% to 70%

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Answers (1)

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Kiley Boone · Answer 1

(C) 10% to 70% (

Step-by-step explanation:

Since at least 40% of the students take German, the Maximum possible percentage of students taking English and not taking German is 60%, but since at least 70% take English, it can be concluded that a minimum of 10% of the students have to take both German and English.

If we assume 30% as minimum number of students taking Italian, and that no student is allowed to take all three language classes, this leaves a maximum of 70% of students that could be taking both English and German.

Therefore, the percentage range for students taking both English and German in the same year goes from 10% to 70%