Problem Solving

In a school, there are three classes ABC, 3% of people have chosen all three, 4% chose the A&B, 6% chose B&C, 2% chose A&C, 23% chose A, 22% chose B, 34 percent chose C. What percent of people did not join any class?

I am getting the answer as 32%. Answer given is 39%. What is your take on this?

check the image. count the numbers inside the circles and subtract from 100.
Answer is 39

Let people that did not join any class = x

For Overlapping Sets:
Total= Group 1 + Group 2 + Group 3 - (Sum of 2 Group Overlaps) -(2* All Three) + Neither

=> 100 = 23+22+34 - 12-6+x
=> 39% - Ans.

HTH

Stacey Koprince wrote:Received a PM asking me to respond. The above two solutions are correct.

erm, can you tell us what you are doing to get 32%? Then we can help to figure out where you're going wrong!

From my studying the EZ books, We should start with the inner most number and subtract the inner most from the each number given until we get the whole thing. This is not applied here ?

Please help.

I do not get the drawing above. I studied this from the EZ solution stat book and thought it was one way to solve three sets. He is not using the same sequence !!!!!

Stacey Koprince wrote:Please spell out exactly what you are doing, step by step, so that we can examine it and help you to figure out what's going on. Actually show us the math!

Here is a similar question. The only difference is that this problem has values instead of percentages. I tried to solve your problem the same way, but couldn't.

In a certain sports club, members are placed in at least one of the three groups. There are 70 members in the soccor group. 80 members are in the hockey group, and 90 members are in the football group. There are 7 members in both soccor and and hockey groups. 8 members in both hockey and football groups, and 9 members in both soccer and football groups. There are 2 members that are in all three groups. How many members are there in total in the sports club ?

First: # of members who are in all three groups = 2

Second:

# of members who are ONLY in Soccer and Hockey groups = 7-2 = 5
# of members who are only in Hockey and football is groups = 8-2 = 6
# of members who are only in soccer and football group = 9-2 = 7

Third:

# of members who are only in soccer group = 70-2-5-7 = 56
# of members who are only in Hockey group = 80-2-5-6 = 67
# of members who are only in football group = 90-2-6-7 = 75

Finally, Total number of members in the club + (56+67+75) + (5+6+7) + (2) = 218


The MGMAT question seems identical, but something is wrong !

Stacey Koprince wrote:The questions are not identical, actually. The MGMAT question asks how many students are in NONE of the classes. In the sample problem you showed, the opening part of the first sentence indicates that every member is in at least one of the groups - in other words, there are ZERO members who are in NONE of the groups. Those are two very different set-ups.

For those who have been struggling with this, perhaps you also didn't notice that the MGMAT question allows some percentage of students to be in NONE of the classes. Factor that in when you solve the problem and see if you can figure it out now.

But aside from this point. The method used to get 23,9, and 14 should be the same ? When I use the method I used in my posted questions, I do not get the same values.