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At the Zamenhof Language School, at least 70% of the students take Eng

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At the Zamenhof Language School, at least 70% of the students take Eng  [#permalink]

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New post 03 Mar 2017, 11:24
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A
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C
D
E

Difficulty:

  95% (hard)

Question Stats:

44% (02:57) correct 56% (02:43) wrong based on 168 sessions

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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%


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Re: At the Zamenhof Language School, at least 70% of the students take Eng  [#permalink]

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New post 03 Mar 2017, 16:30
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The answer is (C) 10% to 70%

Detailed solution in the attachment.
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Re: At the Zamenhof Language School, at least 70% of the students take Eng  [#permalink]

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New post 24 Jul 2018, 08:55
quantumliner wrote:
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
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Re: At the Zamenhof Language School, at least 70% of the students take Eng  [#permalink]

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New post 24 Jul 2018, 10:51
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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.
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Re: At the Zamenhof Language School, at least 70% of the students take Eng  [#permalink]

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New post 26 Jul 2018, 01:21
I still dont understand
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At the Zamenhof Language School, at least 70% of the students take Eng  [#permalink]

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New post 27 Jul 2018, 12:45
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.
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Re: At the Zamenhof Language School, at least 70% of the students take Eng  [#permalink]

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New post 04 Aug 2018, 10:32
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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Re: At the Zamenhof Language School, at least 70% of the students take Eng &nbs [#permalink] 04 Aug 2018, 10:32
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At the Zamenhof Language School, at least 70% of the students take Eng

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