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m04q19 Six students study Russian, Ukrainian & Hebrew [#permalink]
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13 Apr 2008, 15:52
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



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Re: students in a group : fastest way to solve [#permalink]
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13 Apr 2008, 17:04
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Use Set Theory.
Total = A + B + C  (AB+BC+CA) + ABC Given A = 4, B = 3, C = 2, AB+BC+CA = 3, Total = 6 So ABC = Total  A  B  C + (AB+BC+CA) = 6  4  3  2 + 3 = 0
Answer A.



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Re: students in a group : fastest way to solve [#permalink]
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13 Apr 2008, 19:54
abhijit_sen wrote: Use Set Theory.
Total = A + B + C  (AB+BC+CA) + ABC Given A = 4, B = 3, C = 2, AB+BC+CA = 3, Total = 6 So ABC = Total  A  B  C + (AB+BC+CA) = 6  4  3  2 + 3 = 0
Answer A. I tried this and messed up somewhere.



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Re: students in a group : fastest way to solve [#permalink]
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13 Apr 2008, 23:51
kyatin wrote: abhijit_sen wrote: Use Set Theory.
Total = A + B + C  (AB+BC+CA) + ABC Given A = 4, B = 3, C = 2, AB+BC+CA = 3, Total = 6 So ABC = Total  A  B  C + (AB+BC+CA) = 6  4  3  2 + 3 = 0
Answer A. I tried this and messed up somewhere. @Abhijit The colored is not "plus" @kyatin, Total = A+B+C 2*(ABC)  (AB+BC+CA) Let try
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Re: students in a group : fastest way to solve [#permalink]
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14 Apr 2008, 06:35
Sondenso + is correct.
It should be written more like this
Total = A + B + C  { (AB+BC+CA)  3(ABC) }
I believe Abhijit did miss 3 in the equation but has it in the final calculation.



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Re: students in a group : fastest way to solve [#permalink]
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14 Apr 2008, 07:01
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Re: students in a group : fastest way to solve [#permalink]
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14 Apr 2008, 08:40
kyatin wrote: Sondenso + is correct.
It should be written more like this
Total = A + B + C  { (AB+BC+CA)  3(ABC) }
I believe Abhijit did miss 3 in the equation but has it in the final calculation. I have used the correct formula. 3 is not coming from multiplication but from the value mentioned in the question (as given "It is also known that exactly 3 students learn exactly 2 languages"). Also see my explanation earlier, in which I have mentioned what all of these values mentioned in formula should be and we are getting value of ABC and not Total.



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Re: students in a group : fastest way to solve [#permalink]
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14 Apr 2008, 11:57
Abhijit,
You are correct.
\(Total = A + B + C  [ (AB+BC+CA)  (ABC) ]\)
is the right formula.
Thanks Kyatin



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Re: students in a group : fastest way to solve [#permalink]
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14 Apr 2008, 20:36
the way I approached this..
4+3+232(abc)=6
62(abc)=6
2(abc)=0..therefore no one takes all 3 courses..



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Re: students in a group : fastest way to solve [#permalink]
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14 Apr 2008, 23:53
bkk145 wrote: That was neat thread bkk145. Kudos.



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Re: students in a group : fastest way to solve [#permalink]
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15 Apr 2008, 19:03
abhijit_sen wrote: kyatin wrote: Sondenso + is correct.
It should be written more like this
Total = A + B + C  { (AB+BC+CA)  3(ABC) }
I believe Abhijit did miss 3 in the equation but has it in the final calculation. I have used the correct formula. 3 is not coming from multiplication but from the value mentioned in the question (as given "It is also known that exactly 3 students learn exactly 2 languages"). Also see my explanation earlier, in which I have mentioned what all of these values mentioned in formula should be and we are getting value of ABC and not Total. At the moment, I think, I am being confused. The comment I made is from GmatCAt. And now I am advived by the link provided by bkk145. I think I need a thorough material about this concept. Friend, do you have a good material about the Set theory and may you share with me? Many thank and appreciation!
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Re: students in a group : fastest way to solve [#permalink]
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17 Apr 2008, 17:41
bkk145 wrote: Thanks for the link.



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Sets Language [#permalink]
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05 Sep 2008, 00:42
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
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Re: Sets Language [#permalink]
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05 Sep 2008, 00:57
leonidas 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? a) 0 b) 1 c) 2 d) 3 e) 4 A. I solved using a venn diagram, consider x, y and z to be students studying 2 languages and let a be num. of students who study all 3. then 2  x y a + 4 x z a + 3 y z a + x + y + z + a = 6 9  (x +y+z ) 2a = 6 We know that x + y + z = 3 giving us a =0



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Re: Sets Language [#permalink]
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05 Sep 2008, 01:05
Thanks, alpha_plus_gamma. I forgot to include ( x + y + z + a) and was getting incorrect answer....Duh .....Should stop making these kind of mistakes.
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Re: Sets Language [#permalink]
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05 Sep 2008, 01:11
I got A as well. Why is it incorrect?
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Re: Sets Language [#permalink]
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05 Sep 2008, 02:08
I got 0 as well....but using formula....AUBUC = A + B + C  AB  BC  CA + ABC.



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Re: Sets Language [#permalink]
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05 Sep 2008, 03:40
I got A as well:
Total = U + R + H  3(because 3 people study exactly 2 languages, 3 has been counted twice so you need to subtract it once)  2x (because the number of people studying all the 3 languages have been counted 3 times, you want to subtract by twice the amount so that you can count it only once instead of 3 times).
so:
6= H+R+U  3  2x
6 = 2+4+3  3 2x
6= 9  3  2x
6 = 6  2x
0 = 2x
x = 0
Answer A



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Re: Sets Language [#permalink]
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05 Sep 2008, 07:58
Nerdboy wrote: I got A as well. Why is it incorrect? The answer is correct. (A) I mentioned earlier that, I made a silly mistake and lost my ability to think further at 1 am and posted the message
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Re: Sets Language [#permalink]
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05 Sep 2008, 21:36
leonidas 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? a) 0 b) 1 c) 2 d) 3 e) 4 Even i got A Good question !!
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