In order to maximize English and Germany , we minimize Italian and keep the People who picked Italian didn't pick any other subject.

In order to minimize English and Germany , we maximize the people who took both English and Italian. (60%). Now , we could keep Germany separate with 40% but English needs to be 70%. That's why English and Germany share 10% , remaining (100-60-10 = 30) is Germany alone.

The answer is (C) 10% to 70%

Detailed solution in the attachment.

Hi,

I am sorry but I am still confused

Could you please provide the working out for this question.

Regards,

Ritvik

I still dont understand

The maximum number of students who can take English and German will be when the number of students taking Italian is the least.
Therefore, % of students taking Italian = 30%, maximum % of students taking English = 70%. Hence maximum % of students taking both English and German = 70%.

And, minimum number of students taking both English and German will be when the two sets of students taking English and German overlap the least. Let this common group be x.
Therefore 70 + 40 - x = 100%, x = 10%. Hence minimum overlap between given two sets is = 10%.

Therefore, C.

Pretty Straight forward, though took 6 minutes to solve.

1. At least is used for German and English, so we have to be careful about that.
2. Students taking Italian is 30-60%

Worst Case Scenario: (Least German and English)
All German Students took Italian, If 60% Students took Italian, and all 60% took German, then 10% of German Students are left. One could argue that the rest 10% cannot take anything and just take only german but that is not possible since 40% are atleast Students taking German, which shall result in 110%(70% German Atleast(60%Italian+10%only German) +40% Italian), thus 10% should take German So that 100% remains.

Best Case:

30% Took only Italian and thus 70% Took German all the 70% German learning students took English.

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