At the Zamenhof Language School, at least 70% of the students take English each year, at least 40% take German each year, and be

Question

3 months ago

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At the Zamenhof Language School, at least 70% of the students take English each year, at least 40% take German each year, and be

tween 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%

Mathematics

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-02-23T14:33:15+03:00

Answer:

(C) 10% to 70%(

Step-by-step explanation:

Given that at least 40% of the students are learning German, the upper limit of those who might be enrolled in English but not in German is 60%. However, since a minimum of 70% study English, it leads to the conclusion that at least 10% of students must be taking both German and English.

If we consider that at least 30% of students are learning Italian, and assuming that no student is studying all three languages simultaneously, then there is a maximum of 70% of students who could potentially be registered in both English and German.

This means the possible percentage for students enrolled in both English and German ranges from 10% to 70%