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Re: Sets- Language [#permalink]
 06 Sep 2008, 05:20
A for me too!!!
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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?
* 0
* 1
* 2
* 3
* 4
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Re: m04 - languages [#permalink]
10 Sep 2008, 20:02
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?
* 0
* 1
* 2
* 3
* 4 http://gmatclub.com/forum/7-t69804
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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. If it is also known that exactly 3 students study exactly 2 languages, how many students are studying all three languages? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 Source: GMAT Club Tests - hardest GMAT questions Can somebody explain with Venn diagram if possible?
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ConkergMat 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?
Can somebody explain with Venn diagram if possible? r + u + h - (ru+uh+hr) - 2(rhu) + none = 6 4 + 3 + 2 - (3) - 6 + 0 = 2 (rhu) 2 (rhu) = 0 no. of students studying all languages (rhu) = 0 The picture is attached.
Attachments
VENN DIAGRAM.JPG [ 31.09 KiB | Viewed 2705 times ]
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n(RuUuH)= n(R)+n(U)+n(H)-n(RnU)-n(UnH)-n(HnR)+n(RnUnH)
6 = 4 + 3 + 2 - [3] + n(RnUnH)
6 = 6 + n(RnUnH)
0 = n(RnUnH)
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Thanks, a lot!
I got it now.
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6 students in a group study different languages [#permalink]
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.
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Re: 6 students in a group study different languages [#permalink]
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".
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The anwer is 0 . its A
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For a related question and explanation check out: overlapping-sets-99114.html
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Well i did it this way...
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..
Answer: 0
R J
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A fresh outta my set questions yesterday :D
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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
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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. If it is also known that exactly 3 students study exactly 2 languages, how many students are studying all three languages?
a 0
b 1
c 2
d 3
e 4
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Re: overlapping sets [#permalink]
04 Jan 2011, 01:19
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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. Dunno if it is clear  Ans A. 0
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Re: overlapping sets [#permalink]
05 Jan 2011, 01:36
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.
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Re: overlapping sets [#permalink]
05 Jan 2011, 02:29
6= 9 - 3(two languages)+x(all three)+0(who dont study any of the languages)
6=9-3+X+0
X=0---Ans.A
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Re: 6 students in a group study different languages [#permalink]
25 Jun 2011, 10:42
A!
Used the formula
T = G1 + G2 + G3 - (those in 2 of the groups) - 2*(those in all 3 groups)
Nice question!
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Re: 6 students in a group study different languages [#permalink]
25 Jun 2011, 15:04
A U B U C=A+B+C-A intersection B-B intersection C- C intersection A + A intersection B intersection C
=>6 = 4+3+2-3+all three
=> all three = 0
Answer is A.
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Re: 6 students in a group study different languages
[#permalink]
25 Jun 2011, 15:04
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close
