Set theory/Venn diagram prob

[amitansu]

In a colony of 75 people, it's found that 35 people know only 2 of the three languages (German, Latin & French), While 10 people know all the three languages.If every person of the colony knows either of the 3 languages, then how many people know only one language ?

[Neo2000]

10 ppl know all 3 languages

The Red section indicates ppl who know Only 2 languages and it is given that this = 35

The Green section indicates ppl who know only 1 language.

Out of 75 ppl, 10 know all 3 and 35 know 2 which means that 75 - (10+35) = 30 ppl know only 1 language.

[amitansu]

Nice lucid analysis Neo 2000 !!

My interpretation was wrong, i was taking 35 as intersection pf any two of the languages, i.e I took G and L = 35 and you know all wrong attempts after that !!

Thank you very much.

[AleksandrM]

You don't really need a venn diagram for this one. If it said that x know german, y know latin, and z know french, and then w know all three, then how many etc etc etc. In this case it is as simple as subtraction. We are not told that there is group a of people that know neither, so we just ignore it. However, we wouldn't ignore the lack of this piece of information on a DS problem.

75 - 35 - 10 = 30.