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To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." -Edward Bulwer Lytton

6 students in a group study different languages as specified: Russian: 4 Ukrainian: 3 Hebrew: 2 Each student studies at least 1 language. It is also known that exactly 3 students learn exactly 2 languages. How many students are studying all languages? a) 0 b) 1 c) 2 d) 3 e) 4

6 students in a group study different languages as specified:

* Russian: 4 * Ukrainian: 3 * Hebrew: 2

Each student studies at least 1 language. It is also known that exactly 3 students learn exactly 2 languages. How many students are studying all languages?

6 students in a group study different languages as specified:

* Russian: 4 * Ukrainian: 3 * Hebrew: 2

Each student studies at least 1 language. It is also known that exactly 3 students learn exactly 2 languages. How many students are studying all languages?

6 students in a group study different languages as specified:

* Russian: 4 * Ukrainian: 3 * Hebrew: 2

Each student studies at least 1 language. If it is also known that exactly 3 students study exactly 2 languages, how many students are studying all three languages?

6 students in a group study different languages [#permalink]

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30 Aug 2010, 11:11

6 students in a group study different languages as specified:

Russian: 4 Ukrainian: 3 Hebrew: 2

Each student studies at least 1 language. If it is also known that exactly 3 students study exactly 2 languages, how many students are studying all three languages?

0 1 2 3 4

How can we derive the answer with the below formula?

Total = n(A) + n(B) + n(C) – 2(Exactly 2) – 2 (A n B n C) + Neither.

Re: 6 students in a group study different languages [#permalink]

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30 Aug 2010, 11:28

I normally use Venn diagram, however isn't the formula is Total = n(A) + n(B) + n(C) – (Exactly 2) – 2 (A n B n C) + Neither ? That gives the answer "0".

6 students and 9 places up for grabs ( as R=4,U=3,H=2)... Now exactly 3 students study exactl;y 2 subjects..tht means 3x2=6 places out of the total 9.... 3 places remain...and 3 students remain. Since every student studies atleast one language, and only 3 places remain..therefore no single student studies all 3 languages..

like in mgmat book they have solved some questions by table method while others through Venn diagram method.When i look at an overlapping set question,i get confused as which one of the two methods to apply.Any inputs

6 students in a group study different languages as specified:

Russian: 4 Ukrainian: 3 Hebrew: 2 Each student studies at least 1 language. If it is also known that exactly 3 students study exactly 2 languages, how many students are studying all three languages?

yep it is 0. Students who are taking 2 languages: 1 stud(Rus, Ukr) 1 stud(Rus, Heb) 1 stud(Ukr, Rus)=>in this case 2 rus+1 urk+1 heb=4, if one takes 3 languages, then one student will be left with 0. , so no one can take three languages. In other cases, still no one can take three languages.