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

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

by BTGmoderatorLU » Tue Nov 10, 2020 11:03 am

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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 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%

The OA is C
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Re: At the Zamenhof Language School, at least 70% of the students take English each year, at least 40% take...

by Scott@TargetTestPrep » Tue Nov 17, 2020 2:12 pm
BTGmoderatorLU wrote: ↑
Tue Nov 10, 2020 11:03 am
 Source: Magoosh

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%

The OA is C
Solution:

Let’s assume that there are 100 students at Zamenhof Language School. To determine the smallest number of students who take both English and German, notice that even if we choose the smallest possible values of 70 and 40 for the number of students who take English and German, respectively, the smallest value for the number of students who take both courses is 70 + 40 - 100 = 10. Indeed, if 10 students take both English and German, 30 students take German only, 30 students take both Italian and English and the remaining 30 students take English only, we see that all the percentage requirements in the question are satisfied. This shows that the smallest percentage for the students who take both English and German is 10%.

We only need to decide between C and D; in other words, we only need to decide whether the greatest percentage for the students who take both English and German is 70 or 100. Clearly, the percentage of the students who take both English and German cannot be 100 because otherwise, there can be no students who take Italian (since no students take more than two languages). To verify that a value of 70% is possible for “both English and German”, assume that all 100 students take English, 70 take German in addition to English and 30 take Italian in addition to English. Once again, every requirement in the question is satisfied, and this shows that 70 is the greatest possible percentage for the students who take both English and German.

Answer: C

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Re: At the Zamenhof Language School, at least 70% of the students take English each year, at least 40% take...

by deloitte247 » Thu Nov 19, 2020 11:31 am
Since we have at least 40% of students taking German, the maximum possible number of students taking English and not German will be (100 - 40)% = 60% but since at least 70% take English, the minimum number of students taking both German and English = (70 - 60)% = 10%
Between 30% and 60% of students take Italian so assuming that the maximum number of students taking Italian is 30% and since no student is allowed to take all these languages, then the maximum number of students taking both English and German = (100 - 30) % = 70%

Therefore, the % range of students taking both English and German is from 10% to 70%

Answer = C
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