GMAT 3 overlapping sets problem

[luisete2]

I'm way beyond stuck with this problem...

In a certain school with 50 students, the school offers economics, mathematics, and
statistics in the first semester and finance in the second semester. 40 students take
economics, 30 students take mathematics, and 45 students take either economics or
mathematics. 15 students do not take statistics. No students take exactly one course
from these three classes in the first semester. If the finance class’s prerequisite courses
are mathematics, economics, and statistics, how many students are eligible to take
finance?

Applying 2 set theory between mathematics and economics I've gotten to the point that students studying both economics and mathematics are 25. I cannot proceed further than that; can someone lend me a hand?

The solution is 15. Thanks in advance!

 

[Deleted member 4993]

I'm way beyond stuck with this problem...

In a certain school with 50 students, the school offers economics, mathematics, and
statistics in the first semester and finance in the second semester. 40 students take
economics, 30 students take mathematics, and 45 students take either economics or
mathematics. 15 students do not take statistics. No students take exactly one course
from these three classes in the first semester. If the finance class’s prerequisite courses
are mathematics, economics, and statistics, how many students are eligible to take
finance?

Applying 2 set theory between mathematics and economics I've gotten to the point that students studying both economics and mathematics are 25. I cannot proceed further than that; can someone lend me a hand?

The solution is 15. Thanks in advance!

Although not asked in the problem I would first attempt to draw a Venn diagram to graphically interpret the problem.

 

[luisete2]

Although not asked in the problem I would first attempt to draw a Venn diagram to graphically interpret the problem.

I did that already, but I'm not sure if it's okay with the 25.

 

[lex]

Write out your facts:
[MATH]\boxed{\;\;\text{Total} \;\; 50\;\;}[/MATH]E 40
M 30
E [MATH]\cup M[/MATH] 45
[MATH]\overline{S}[/MATH] 15
No-one takes only one course.

Sometimes the negative is more useful!
[MATH]\boxed{\;\;\text{Total} \;\; 50\;\;}[/MATH]
No-one takes only one course.
[MATH]\overline{E\cup M}\;\;[/MATH] 5
[MATH]\overline{E}[/MATH] 10
[MATH]\overline{M}[/MATH] 20
[MATH]\overline{S}[/MATH] 15
Total 50

Now fill in the diagram using these 6 facts, in the order just given. (The first is done for you)!

 

[luisete2]

Well, I hadn't thought of it that way. I tried to use the opposite data in a different formula with no success. I filled the diagram, however, E∪M still slips a bit for me, I do not know where to place it. Is it students that have done simultaneously mathc and economics or the ones that directly haven't gotten any, but where does it go?

Sorry if I'm a bit short... this field is not fresh for me and I'm on a rush of study around many other topics.

 

[pka]

In the Venn diagram you did only one area is correct: \(\#(M\cap E\cap\overline{S})=15\)
I will tell you that \(\#(M\cap E\cap S)=10\).
Please correct and post a new diagram.

 

[lex]

Well, I hadn't thought of it that way.

I notice you haven't used the information that I sent and you have re-posted the same Venn Diagram. I assume that means that you don't know how to use Venn diagrams. I would recommend learning that, because it is a very useful technique.
There's no point in me continuing with Venn Diagrams in that case, until you have revised them.
However I have made an equivalent 'table' form of the Venn Diagram, which you could use. Below it I have written out my list of facts again. Use it to fill in the final column 'People' of the first table.



Table of Facts