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overlapping sets-challenge

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overlapping sets-challenge

by Night reader » Thu Dec 02, 2010 2:59 am
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

I was unable to solve this
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by Rahul@gurome » Thu Dec 02, 2010 3:16 am
Night reader wrote: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

I was unable to solve this
Number of people graduated from college = N
Number of people received a degree = N/3
Number of people received a degree and graduated from a school = (1/4)*(N/3) = N/12

Thus number of people who graduated from college and did not both receive a degree and graduated from a school = (N - N/12) = 11N/12

The correct answer is A.
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by GMATGuruNY » Thu Dec 02, 2010 4:15 am
Night reader wrote: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

I was unable to solve this
We can plug in our own value for N. We should choose a number that is divisible by the denominators of the two fractions in the problem (1/3 and 1/4).

Let N = 3*4 = 12.
Received a degree = 1/3 * 12 = 4.
Received a degree and graduated from one of the six schools = 1/4 * 4 = 1.
Since only 1 person both received a degree and graduated from one of the six schools, the number who didn't do both = 12-1 = 11. This is our target.

Now we plug N=12 into all the answers to see which yields our target of 11.

Only answer choice A works:
11/12*N = 11/12 * 12 = 11.

The correct answer is A.
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by pesfunk » Fri Feb 04, 2011 8:55 am
One quick way of doing this can be as below:

since we see 2 denominators 3 and 4, i will take a big common multiple...say 60


so out of 60, 20 received a degree in applied science. out of this 20, 4 graduated from school.

thus, the reverse combination of 5 is 60-5 = 55

if we take the first option itself : 60 * 11 / 12 = 55.
Night reader wrote: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

I was unable to solve this
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by VivianKerr » Fri Feb 04, 2011 10:40 am
These questions can also be solved using a Venn diagram to make sense of the information:

Image

The key to understanding this question lies in the last sentence:

who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

We have two categories to sum: the people who ONLY received a science degree but NOT from one of the 6 schools, and the people who ONLY went to the 6 schools but did NOT receive a science degree. I made up variables for these categories (x and y).

If N = 12, there are 4 applied science students, 1 of which is both. That means x = 3. If 4 students are applied science, then 12-4 = 8 are from one of the six states but NOT applied science. y = 8.

3 + 8 = 11

So we are looking for an answer choice that gives us 11 when N = 12; the answer is A.
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by Night reader » Fri Feb 04, 2011 9:41 pm
Night reader wrote: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

I was unable to solve this
of course it's simple calc, I was stamped in Dec :)
1/3 N are awarded AS degrees
1/3N * 1/4 are graduates of NA states --> 1/12 N both grads and NA states
(1-1/12)N=11/12 N
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by saleem.kh » Wed Jun 08, 2011 5:37 am
VivianKerr wrote:These questions can also be solved using a Venn diagram to make sense of the information:

Image

The key to understanding this question lies in the last sentence:

who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

We have two categories to sum: the people who ONLY received a science degree but NOT from one of the 6 schools, and the people who ONLY went to the 6 schools but did NOT receive a science degree. I made up variables for these categories (x and y).

If N = 12, there are 4 applied science students, 1 of which is both. That means x = 3. If 4 students are applied science, then 12-4 = 8 are from one of the six states but NOT applied science. y = 8.

3 + 8 = 11

So we are looking for an answer choice that gives us 11 when N = 12; the answer is A.
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by cans » Wed Jun 08, 2011 6:01 am
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?
Graduation=N
degree in applied science (D) = n/3
D + graduation from 6 north eastern states (GS)= (1/4)*(n/3) = n/12
thus neither D nor GS = n - n/12 = 11n/12
IMO A
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by gmat3last » Mon Jun 20, 2011 11:16 am
ok here i was completely stumped from a different angle. I read the question as the segment who is neither an applied science graduate NOR a NE school graduate...instead of reading it as the segmentS who did not do BOTH 1) apply science graduate and 2) NE school graduate.
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by winniethepooh » Mon Jun 20, 2011 10:35 pm
Same here,tricky one, but makes sense, awesome work experts!!
Vivian, Mitch and Rahul, I wonder how you guys actually crack that!
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by amit2k9 » Wed Jun 22, 2011 4:01 am
n- 1/4*1/3*n = 11n/12 it is.
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by navami » Wed Jun 22, 2011 5:24 am
yes 11N/12 is the ans
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by prashant misra » Thu Dec 08, 2011 1:33 am
Can anyone please explain me this question in more detail through a table or flowchart i am still not able to get it.
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by ronnie1985 » Fri Apr 06, 2012 9:56 am
11n/12
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by rjain84 » Wed Feb 20, 2013 4:59 pm
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)
------
Image

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