Problem Solving

In a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?


Guyzzz... according to me the answer comes out to 19. Is it correct???

Hi,
e1 - no.of students registered for exactly one class
e2 - no.of students registered for exactly two classes
e3 - no.of students registered for exactly three classes
e1+e2+e3 = 68
e1+2e2+3e3 = 25+25+34=84
So, e2+2e3 = 16
but, e3 = 3. So, e2 = 10

total 68
H,M,E
H=25;M=25;E=34
H&m&e=3
exactly 1 + exactly 2 + exactly 3 =total = 68
also exactly 1 + 2*exactly 2 + 3*exactly3 = one each = 25+25+34 = 84
Thus solving, exactly2 = 10

Frankenstein wrote:Hi,
e1 - no.of students registered for exactly one class
e2 - no.of students registered for exactly two classes
e3 - no.of students registered for exactly three classes
e1+e2+e3 = 68
e1+2e2+3e3 = 25+25+34=84
So, e2+2e3 = 16
but, e3 = 3. So, e2 = 10

Would like to know how did we arrive at e1+2e2+3e3 = 25 + 25 + 34 ?

Many of the questions with which you're practicing have been previously discussed on this board. The BTG search tool is very useful.

Here are a couple of threads discussing this question:

https://www.beatthegmat.com/mgmat-cat-2- ... 47933.html

and

https://www.beatthegmat.com/3-sets-prob-t35079.html

the second even has a pretty picture!

edit: typo!

Stuart Kovinsky wrote:Many of the questions with which you're practicing have been previously discussed on this board. The BTG search tool is very useful.

Here are a couple of threads discussion this question:

https://www.beatthegmat.com/mgmat-cat-2- ... 47933.html

and

https://www.beatthegmat.com/3-sets-prob-t35079.html

the second even has a pretty picture!

tHank you !

Thank you so much guyzz.. for a wonderful explanation!!!!