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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?
Re: m04 - languages [#permalink]
10 Sep 2008, 19:02
sarzan wrote:
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 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?
Can somebody explain with Venn diagram if possible?
6 students in a group study different languages [#permalink]
30 Aug 2010, 10:11
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]
30 Aug 2010, 10:28
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?
Re: overlapping sets [#permalink]
04 Jan 2011, 00:19
1
This post received KUDOS
A for me!
The question says that 3 students study exactly 2 languages each. THerefore from the total of languages being studied by the 6 individual, 9
9-6=3
There are 3 people left for 3 languages left. Moreover, every person has to study at least one language so it is no feasible to have one person studying 3 languages and the other 2 studying none.
Re: overlapping sets [#permalink]
05 Jan 2011, 00:36
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.