gmat club overlapping sets

bblast wrote: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

oa-0



anybody with triple set matrix equation for this one ? I could solve by short cut in the test but later tried by triple set equation and got stuck. I remember having had to guess a triple set question in GMAT-1. the thought is still in my mind . :/

[spoiler]my equation - 9-3x-2(p+q+r) = 6
given p+q+r = 3.
x=3 which is wrong.[/spoiler]

Here is the formula for 3 overlapping groups in which sometimes 2 groups overlap and sometimes all 3 groups overlap:

T = G1 + G2 + G3 - (those in 2 of the groups) - 2*(those in all 3 groups)

The big idea with overlapping groups is to subtract the overlaps. When we count everyone in the 3 groups, those in 2 of the groups will be counted twice, so they need to subtracted from the total once. Those in all 3 groups will be counted 3 times, so they need to be subtracted from the total twice.

In the problem above:
T = 6
G1+G2+G3 = Russian + Ukrainian + Hebrew = 4+3+2 = 9
Number studying exactly 2 languages = 3
Number studying all 3 languages = x

Plugging into the formula, we get:

6 = 9 - 3 - 2x
6 = 6 - 2x
0 = -2x
x = 0.

The correct answer is A.

bblast,

go thru the below link whn u have time. it gives u some good insights into oevrlaing sets formulas wth explanations. i found it useful.

https://gmatclub.com/forum/formulae-for- ... 69014.html

cheers

I tried to solve it by making equations, somehow did it, but later on figured out that it could be solved with some logic..

R U H
4+3+2=9
total 9

A B C D E F
1+1+1+1+1+1=6 Each student studies at least 1 language
1+1+1=3 exactly 3 students study exactly 2 languages
total 9

answer 0 students are studying all three languages?

I approached this problem with a sort of table approach.

Number of those studying languages: 6
Number of classes taken among the students: 4+3+2 = 9
And we have three students taking studying exactly two languages: 3x2=6
Each student studies at least one language

(Classes) 9-6 = 3; (Students) 6-3 = 3, so there are three more students to fill the three remaining spots. Since each student takes at least one class, each of the remaining three students must take only one class. No students are left. Answer is A.