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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?

Re: students in a group : fastest way to solve [#permalink]

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13 Apr 2008, 17:04

4

This post received KUDOS

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

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?

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: 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

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
_________________

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.

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!
_________________

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
_________________

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

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

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).