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m04q19- Six students study Russian, Ukrainian & Hebrew

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Manager
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06 Sep 2008, 05:20
A for me too!!!
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10 Sep 2008, 18:44
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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Director
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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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24 Jan 2009, 22:41
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

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

Can somebody explain with Venn diagram if possible?

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26 Jan 2009, 13:52
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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.
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VENN DIAGRAM.JPG [ 31.09 KiB | Viewed 3280 times ]

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27 Jan 2009, 11:14
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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28 Jan 2009, 06:21
Thanks, a lot!
I got it now.

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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.

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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 ?

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11 Oct 2010, 07:08
The anwer is 0 . its A

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11 Oct 2010, 11:16
For a related question and explanation check out:

overlapping-sets-99114.html

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11 Oct 2010, 12:48
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..

R J

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11 Oct 2010, 22:29
A

fresh outta my set questions yesterday :D
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14 Oct 2010, 19:53
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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03 Jan 2011, 17:19
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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04 Jan 2011, 01:19
1
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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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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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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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Manager
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Re: 6 students in a group study different languages [#permalink]

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

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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

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Re: 6 students in a group study different languages   [#permalink] 25 Jun 2011, 15:04

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