overlapping sets-challenge

manasgoswami1 wrote:Hi,

i had a query:

there should be four cases according to the grid/tic tac toe method but i'm unable to solve it

1) those who got degree and went to school = N/12
2) those who got degree but did not go to school= 3N/12
3) those who neither got degree nor went to school= ?
4)those who went to school but did not get a degree=?

Can anyone help me through this method?

Regards

Here's the Double Matrix method step-by-step:

Note: This technique can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- degree (applied sciences or not)
- school location (northeastern state or not)

In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

(A) 11N/12
(B) 7N/12
(C) 5N/12
(D) 6N/7
(E) N/7

In 1997, N people graduated from college.


1/3 of them received a degree in the applied sciences


Of those (1/3)N students, 1/4 graduated from a school in one of six northeastern states.

In other words, (1/12)N students have a degree in applied sciences and graduated from a northeastern school.

Which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?
If the box that has (1/12)N students in it represents the students with a degree in applied sciences and graduated from a northeastern school, then the remaining boxes (shaded in blue) must represent the students who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.


Since all 4 boxes must add to N (the total number of students), the 3 shaded boxes must add to [spoiler](11/12)N[/spoiler].

Answer = A

Cheers,
Brent

To learn more about Double Matrix method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Then try these additional practice questions that can be solved using the Double Matrix Method:
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html

manasgoswami1 wrote:Hi Brent,

Many thanks for same. I could not comprehend that all the 3 boxes are the answer and i was looking for one

it's 2 am here and maybe fatigue is taking its toll on me:)

thanks again

regards

Let's look at it this way.
Let's say there are 100 people in a room, and I say "raise your hand if you received an applied sciences degree AND graduated from a northeastern school"
If 25 people raise their hands, what can we say about the 75 people who aren't raising their hands?
These people did NOT both receive an applied sciences degree AND graduate from a northeastern school." These are the people that we're looking for.
So, of the 100 people, 25 met both conditions. This means 100-25 = # of people who didn't meet both conditions.

Likewise, of the N people, (1/12)N people met both conditions. This means N - (1/12)N = # of people who didn't meet both conditions.

Does that help?

Cheers,
Brent