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Re: 6 students in a group study different languages [#permalink]
25 Jun 2011, 14:23

Substitution is fast but inelegant. Sub 0 for all three - 0 students used. Then subtract the 3 paired students from 4 Russian and 3 Ukrainian leaving 1 Russian and 2 Hebrew student. 3 pairs + 1 Russian + 1 Hebrew = 6 students. 0 yields 6=6 students

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. 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

i dont think we need a venn diagram here..

from given - 1) each student studies atleast 1 language, so 6 students studies 6 languages atleast... 2) 3 students studies exactly 2 languages.. = 6 so alltogether from the info, 6 students studies 6+3 = 9 languages (we are adding 3 because 1 language isalready considered before)..

now its also given that total 4+3+2 =9 languages are studied.. so none student studies all 3 languages. answer A.

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

I believe this is correct, but please help me find the flaw in my reasoning here...if it exists

1. From the info we know all 6 students have at least 1 language and 3 have exactly two. Therefore we have (3+6) =9 languages at minimum. Because we know 3 have exactly 2, the number studying all three must be 3 or less, so rule out d.

2. Because the numbers next to the languages added together represent the total of all possible combinations, when we add them we get the same number as with the requirements above. So, we know that the requirements must be 1 language for 3 and 2 languages for 3. Therefore, we have 0 students studying all 3.

Re: m04q19- Six students study Russian, Ukrainian & Hebrew [#permalink]
14 Oct 2011, 05:22

I Have a special formula for this case..... S-X=TWO+2*THREE Here s is the sum of sets which equals to 4+3+2=9 x is the no.of people who study at least one language which is 6 bcoz six people r there nd each reads at least one language so 6*1=6 nd exactly 3 students study 2 language.. so S=9,X=6,No.of student exactly studying two language=3 so 9-6=3+2*3 which equals to 0...