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In 1997, N people graduated from college. If 1/3 of them

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In 1997, N people graduated from college. If 1/3 of them [#permalink]

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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 this question How can we assume that there a zero (0) people who have no degree in applied science and no graduates in one of six NE states? Its not specified in the problem.

4 equations

Degree in Applied Science + Graduate in six schools = Equation A
Degree in Applied Science + Did not graduate from six schools = Equation B
No Degree in Applied Science + Graduate in six schools = Equation C
No Degree in Applied Science + Did not graduate from six schools = Equation D

I think, the problem is assuming "Equation D" to be Zero. BUt I am confused as how to interpret this?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 05 Jun 2013, 00:59, edited 2 times in total.
Renamed the topic and edited the question.

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Re: In 1997, N people graduated from college. If 1/3 of them [#permalink]

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New post 04 Jun 2013, 21:39
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maaadhu 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

[Reveal] Spoiler:
In this question How can we assume that there a zero (0) people who have no degree in applied science and no graduates in one of six NE states? Its not specified in the problem.

4 equations

Degree in Applied Science + Graduate in six schools = Equation A
Degree in Applied Science + Did not graduate from six schools = Equation B
No Degree in Applied Science + Graduate in six schools = Equation C
No Degree in Applied Science + Did not graduate from six schools = Equation D

I think, the problem is assuming "Equation D" to be Zero. BUt I am confused as how to interpret this?


Go one statement at a time:

"In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, "

Degree in applied sciences = N/3

"and, of those, 1/4 graduated from a school in one of six northeastern states,"

Degree in applied sciences and graduated from a school in one of six northeastern states = (N/3) * (1/4) = N/12

"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?"

So N people graduated from college and N/12 got a degree in applied sciences and graduated from one of six northeastern states (i.e. N/12 did both).
Hence the other N - N/12 = 11N/12 did not do both (receive a degree in applied sciences and graduated from a school in one of 6 northeastern states). They could have done one of them but they certainly did not do both.


It's similar to this simpler question:

100 students study in this school. 10 study in Nursery and of those 10, 4 are less than 3 yrs of age. So how many students in this school are such that they are not both - in Nursery and less than 3 yrs of age?
We will find the number of students who are both - in Nursery as well as less than 3 yrs of age. We know there are 4 such students. So the rest of the 100 - 4 = 96 students are such that either they are not in Nursery or they are not less than 3 yrs or they are not both (say they are in standard 1 and 6 yrs old). Our answer will be 96.
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Re: In 1997, N people graduated from college. If 1/3 of them [#permalink]

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New post 05 Jun 2013, 01:15
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maaadhu 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

In this question How can we assume that there a zero (0) people who have no degree in applied science and no graduates in one of six NE states? Its not specified in the problem.

4 equations

Degree in Applied Science + Graduate in six schools = Equation A
Degree in Applied Science + Did not graduate from six schools = Equation B
No Degree in Applied Science + Graduate in six schools = Equation C
No Degree in Applied Science + Did not graduate from six schools = Equation D

I think, the problem is assuming "Equation D" to be Zero. BUt I am confused as how to interpret this?


Karishma has already given an excellent analysis of the question.

As for your doubt: out of 11N/12, some received a degree, some applied and some did none of those (neither received a degree nor applied), but they certainly did not do both.

Consider this: assume N=12. Then 12/3=4 received a degree and 4/4=1 did both (received a degree and applied), thus 12-1=11 did not do both. Out of those 11, some received a degree (4), some applied (?) and some did none of those (?) (neither graduated nor applied), but they certainly did not do both.

Hope it's clear.
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Kudos [?]: 133204 [1], given: 12439

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Re: In 1997, N people graduated from college. If 1/3 of them [#permalink]

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New post 05 Jun 2013, 12:24
Thank You Karishma & Bunuel.

Sometimes understanding the question is the hard part.
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Re: In 1997, N people graduated from college. If 1/3 of them [#permalink]

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New post 13 Jan 2014, 03:31
VeritasPrepKarishma wrote:
maaadhu 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

[Reveal] Spoiler:
In this question How can we assume that there a zero (0) people who have no degree in applied science and no graduates in one of six NE states? Its not specified in the problem.

4 equations

Degree in Applied Science + Graduate in six schools = Equation A
Degree in Applied Science + Did not graduate from six schools = Equation B
No Degree in Applied Science + Graduate in six schools = Equation C
No Degree in Applied Science + Did not graduate from six schools = Equation D

I think, the problem is assuming "Equation D" to be Zero. BUt I am confused as how to interpret this?


Go one statement at a time:

"In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, "

Degree in applied sciences = N/3

"and, of those, 1/4 graduated from a school in one of six northeastern states,"

Degree in applied sciences and graduated from a school in one of six northeastern states = (N/3) * (1/4) = N/12

"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?"

So N people graduated from college and N/12 got a degree in applied sciences and graduated from one of six northeastern states (i.e. N/12 did both).
Hence the other N - N/12 = 11N/12 did not do both (receive a degree in applied sciences and graduated from a school in one of 6 northeastern states). They could have done one of them but they certainly did not do both.


It's similar to this simpler question:

100 students study in this school. 10 study in Nursery and of those 10, 4 are less than 3 yrs of age. So how many students in this school are such that they are not both - in Nursery and less than 3 yrs of age?
We will find the number of students who are both - in Nursery as well as less than 3 yrs of age. We know there are 4 such students. So the rest of the 100 - 4 = 96 students are such that either they are not in Nursery or they are not less than 3 yrs or they are not both (say they are in standard 1 and 6 yrs old). Our answer will be 96.


Hi Karishma,

Is there anyway that this question can be solved by putting together a table/ chart for "Applied Sciences" and "Graduated from NE states." I used N as 60 that gave following chart ==>

-------------->Allied Sc<---------->No Allie Sc<---->Total
NE states------->5 <---------------->?
No NE State--->15<---------------->x
Total------------>20<----------------> 40<----------->60

I am thinking that question is to solve for x . But if I substitute value from ans choices I am unable to get the desired result.

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In 1997, N people graduated from college. If 1/3 of them [#permalink]

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maaadhu 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



Here's the Double Matrix Method with step-by-step details:

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.
Image

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

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

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

Answer =
[Reveal] Spoiler:
A


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Re: In 1997, N people graduated from college. If 1/3 of them [#permalink]

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Re: In 1997, N people graduated from college. If 1/3 of them   [#permalink] 06 Oct 2017, 09:31
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