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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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Updated on: 04 Jun 2013, 23:59
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Difficulty:

55% (hard)

Question Stats:

64% (02:13) correct 36% (02:30) wrong based on 222 sessions

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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?

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Originally posted by maaadhu on 04 Jun 2013, 11:52.
Last edited by Bunuel on 04 Jun 2013, 23:59, 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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04 Jun 2013, 20:39
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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?

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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05 Jun 2013, 00:15
2
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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Re: In 1997, N people graduated from college. If 1/3 of them  [#permalink]

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05 Jun 2013, 11:24
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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13 Jan 2014, 02:31
VeritasPrepKarishma 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?

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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Updated on: 17 Apr 2018, 07:01
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Top Contributor
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.

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 (11/12)N.

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Originally posted by GMATPrepNow on 22 Sep 2016, 11:36.
Last edited by GMATPrepNow on 17 Apr 2018, 07:01, edited 1 time in total.
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Re: In 1997, N people graduated from college. If 1/3 of them  [#permalink]

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16 Jan 2018, 12:20
Hi All,

This question can be solved by TESTing VALUES. Even before we read the prompt, the answer choices certainly appear to provide some context for what the perfect Value to TEST would be (probably 12 or 7, since the answer choices are all fractions with one or the other of those numbers as the denominator). Once we read through the information involving the two fractions, it seems pretty clear that we should be TESTing 12...

IF...
1/3 = 4 received a degree in applied sciences
1/4 (of those 4) = 1 graduated from a school in a northeastern state

We're asked for the number of people who did NOT receive a degree in applied sciences and graduate from one of those states. Since 1 of the 12 fit BOTH descriptions, 11 of the 12 do NOT. TESTing N = 12 leads to just one matching answer...

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

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05 Sep 2018, 20:04
[quote="VeritasKarishma"][quote="maaadhu"]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

stem says AND not OR ,
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Re: In 1997, N people graduated from college. If 1/3 of them  [#permalink]

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18 Oct 2018, 12:40
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

$$?\,\,\,:\,\,\,\# \,\,\,\,{\text{not}}\,\,\,\left[ {\,\,\left( {{\text{applied}}\,\,{\text{sciences}}\,\,{\text{degree}}} \right)\,\,{\text{AND}}\,\,\left( {{\text{in}}\,\,{\text{one}}\,\,{\text{of}}...} \right)\,\,} \right]\,\,\,\,\, = \,\,\,\,\# \,\,\,\left[ {\,\,\left( {{\text{not}}\,\,{\text{applied}}\,\,{\text{sciences}}\,\,{\text{degree}}} \right)\,\,{\text{OR}}\,\,\left( {{\text{not}}\,\,{\text{in}}\,\,{\text{one}}\,\,{\text{of}}...} \right)\,\,} \right]\,$$

$$N\,\,:\,\,{\text{graduated}}\,\,\,\, \to \,\,\,\,\left\{ \begin{gathered} \,\frac{1}{3}N\,\,:\,\,{\text{applied}}\,\,{\text{sciences}}\,\,{\text{degree}}\,\,\,\, \to \,\,\,\,\left\{ \begin{gathered} \,\frac{1}{4}\left( {\frac{1}{3}N} \right)\,\,\,:\,\,{\text{in}}\,{\text{one}}\,{\text{of}}\,\,... \hfill \\ \,\boxed{\frac{3}{4}\left( {\frac{1}{3}N} \right)}\,\,:\,\,{\text{not}}\,\,{\text{in}}\,\,{\text{one}}\,\,{\text{of}}\,\,... \hfill \\ \end{gathered} \right. \hfill \\ \,\boxed{\frac{2}{3}N}\,:\,\,{\text{not}}\,\,{\text{applied}}\,\,{\text{sciences}}\,\,{\text{degree}}\,\,\left( {{\text{and}}\,{\text{not}}\,\,{\text{in}}\,\,{\text{one}}\,\,{\text{of}}\,\,...} \right)\,\, \hfill \\ \end{gathered} \right.$$

$$?\,\,\mathop = \limits^{\left( * \right)} \,\,\,\frac{3}{4}\left( {\frac{1}{3}N} \right) + \frac{2}{3}N = \frac{{1 \cdot 3}}{{4 \cdot 3}}N + \frac{{2 \cdot 4}}{{3 \cdot 4}}N = \frac{{11}}{{12}}N$$

(*) Important: the two parcels are related to mutually exclusive events!

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: In 1997, N people graduated from college. If 1/3 of them &nbs [#permalink] 18 Oct 2018, 12:40
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