overlapping sets-challenge

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.

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

These questions can also be solved using a Venn diagram to make sense of the information:



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.

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

VivianKerr wrote:These questions can also be solved using a Venn diagram to make sense of the information:



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.

THANK YOU FOR EXPLANATION USING DIAGRAM. CAN YOU PLEASE EXPLAIN USING MATRIX TABLE. I AM TRYING TO DO IT USING MATRIX AS SECOND OPTION BUT NOT ABLE TO FIND RIGHT SOLUTION.

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

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.

Same here,tricky one, but makes sense, awesome work experts!!
Vivian, Mitch and Rahul, I wonder how you guys actually crack that!

n- 1/4*1/3*n = 11n/12 it is.

yes 11N/12 is the ans

Can anyone please explain me this question in more detail through a table or flowchart i am still not able to get it.

11n/12
QED

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