Overlapping sets questions

[rjain84]

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

Can anybody please point out what am I missing in my approach? I am using matrix method to solve it.

Let, Graduate students who got Applied Science degree = AS
Graduate students who did not get Applied Science degree = Not AS
Graduate students who were from north-eastern states = NES
Graduate students who were not from north-eastern states = NOT NES

Matrix (please click on image to see the full matrix)
------


We want to calculate x but according to the matrix it can't be determined. Please guide what am I missing here?

[Brent@GMATPrepNow]

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

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(north eastern state or not)

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

Aside: For more information about the Double Matrix method and some additional practice questions, check out these 3 BTG articles:
- 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

[GMATGuruNY]

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

Can anybody please point out what am I missing in my approach? I am using matrix method to solve it.

Let, Graduate students who got Applied Science degree = AS
Graduate students who did not get Applied Science degree = Not AS
Graduate students who were from north-eastern states = NES
Graduate students who were not from north-eastern states = NOT NES

Matrix (please click on image to see the full matrix)
------


We want to calculate x but according to the matrix it can't be determined. Please guide what am I missing here?

You don't need to complete the grid to answer the question.
According to the top left corner of your grid, (1/12)N of the students are both AS and NES.
Thus, the fraction that are NOT both AS and NES = N - (1/12)N = (11/12)N.

The correct answer is A.

[Brent@GMATPrepNow]

You can find 2 more Double Matrix practice questions (with free video solutions) here:
- https://www.gmatprepnow.com/module/gmat- ... ems?id=920
- https://www.gmatprepnow.com/module/gmat- ... ems?id=943

Cheers,
Brent

[rjain84]

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

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(north eastern state or not)

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

Aside: For more information about the Double Matrix method and some additional practice questions, check out these 3 BTG articles:
- 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

Thanks a ton for the detailed explanation and for providing the links for more practice Brent!

However, I still have a doubt -

The phrase - "who did not both receive a degree in the applied sciences AND graduate from a school in one of six northeastern states?"

I think it means intersection not union (because of AND not OR)

So don't we want the value in the box (2,2) i.e the box in the lower right in the matix and not the values in all the shaded boxes?

[Brent@GMATPrepNow]

Thanks a ton for the detailed explanation and for providing the links for more practice Brent!

However, I still have a doubt -

The phrase - "who did not both receive a degree in the applied sciences AND graduate from a school in one of six northeastern states?"

I think it means intersection not union (because of AND not OR)

So don't we want the value in the box (2,2) i.e the box in the lower right in the matix and not the values in all the shaded boxes?

Let's take a closer look at the phrase: "who did not both receive a degree in the applied sciences AND graduate from a school in one of six northeastern states"

If we ignore the not, we get: "who did both receive a degree in the applied sciences AND graduate from a school in one of six northeastern states"
These students are represented by the top-left box with (1/12)N students.

Once we put the not back into the phrase, we are referring to everybody else.

Cheers,
Brent

[rjain84]

Let's take a closer look at the phrase: "who did not both receive a degree in the applied sciences AND graduate from a school in one of six northeastern states"

If we ignore the not, we get: "who did both receive a degree in the applied sciences AND graduate from a school in one of six northeastern states"
These students are represented by the top-left box with (1/12)N students.

Once we put the not back into the phrase, we are referring to everybody else.

Cheers,
Brent

Gotcha! Your explanation makes perfect sense Brent. Many thanks once again.

[pareekbharat86]

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

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(north eastern state or not)

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

Aside: For more information about the Double Matrix method and some additional practice questions, check out these 3 BTG articles:
- 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

The ques asks to find the prob. selecting students who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

Therefore, we should be looking at the following:







Why am I not correct?[/u]

[Brent@GMATPrepNow]

The ques asks to find the prob. selecting students who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

Therefore, we should be looking at the following:



Why am I not correct?[/u]

The bottom right box that you are referring to represents the number of students who NEITHER received a degree in the applied sciences NOR graduated from a school in one of six northeastern states.

This is not what the question is asking for. We want the number of students who who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

So, if the top-left box represents students who both received a degree in the applied sciences AND graduated from a school in one of six northeastern states, then the remaining 3 boxes represent the number of students who who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

I hope that helps.

Cheers,
Brent

[pareekbharat86]

The ques asks to find the prob. selecting students who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

Therefore, we should be looking at the following:



Why am I not correct?[/u]

The bottom right box that you are referring to represents the number of students who NEITHER received a degree in the applied sciences NOR graduated from a school in one of six northeastern states.

This is not what the question is asking for. We want the number of students who who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

So, if the top-left box represents students who both received a degree in the applied sciences AND graduated from a school in one of six northeastern states, then the remaining 3 boxes represent the number of students who who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

I hope that helps.

Cheers,
Brent

The language of the question stumped me!

Thanks a lot Brent. I am discovering how helpful this website is! Wish you guys all the best.

[bzb]

hi,

I am still in doubt about this question...I tried this other question:

Santa estimates that 10% of the children in the world have been good this year but do not celebrate Christmas, and that 50% of the children who celebrate Christmas have been good this year. If 40% of the children in the world have been good, what percentage of children in the world are not good and do not celebrate Christmas?

the grid I made was like this:







...how is not good and not celebrating christmas different from both not good and not celebrating christmas? I thought that like the given problem about graduates, I should take the entire region (60+10) as neither good nor celebrate x-mss

could someone please point out the difference between them.....

-thanks