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Overlapping sets question

by AndyMann » Sat Jun 22, 2013 11:01 am

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Will really appreciate if anyone can help to solve this question using Double set matrix method.

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

OA: A

Thanks a lot,
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Overlapping sets question

by Brent@GMATPrepNow » Sat Jun 22, 2013 11:05 am
AndyMann wrote:Will really appreciate if anyone can help to solve this question using Double set matrix method.

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

OA: A

Thanks a lot,
Andy
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 (northeastern 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 [spoiler](11/12)N[/spoiler].

Answer = A

Cheers,
Brent

To learn more about Double Matrix method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Then try these additional practice questions that can be solved using the Double Matrix Method:
- 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
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
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by AndyMann » Sat Jun 22, 2013 11:25 am
Dear Brent,

Thanks so much for your prompt reply. Your answers are always so concise and helpful.

I am still little confused with the wording of the question. It says to find "who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states"; Is this not pointing to the box in the double matrix for "Not AS" and "Not NES"?

I am trying to get my head around it that why it's the sum of the 3 blue boxes.

Thanks,
Andy
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by GMATGuruNY » Sat Jun 22, 2013 11:28 am
AndyMann wrote:Will really appreciate if anyone can help to solve this question using Double set matrix method.

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

OA: A
Let N = the LCM of the denominators in the problem = 3*4 = 12.
The number who received a degree in the applied sciences = (1/3)12 = 4.
Of the 4 who received a degree in the applied sciences, the number who graduated in one of the NE states = (1/4)4 = 1.
Since only 1 person both received a degree in the applied sciences and graduated in one of the NE states, the number who did NOT do both = 12-1 = 11. This is our target.

Now we plug N=12 into the answers to see which yields our target of 11.
A quick scan of the answer choices reveals that only A works:
(11N)12 = (11*12)/12 = 11.

The correct answer is A.
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by Brent@GMATPrepNow » Sat Jun 22, 2013 11:58 am
AndyMann wrote:Dear Brent,

Thanks so much for your prompt reply. Your answers are always so concise and helpful.

I am still little confused with the wording of the question. It says to find "who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states"; Is this not pointing to the box in the double matrix for "Not AS" and "Not NES"?

I am trying to get my head around it that why it's the sum of the 3 blue boxes.

Thanks,
Andy
Good question.
The top-left box refers to students who both received a degree in the applied sciences and graduate from a school in one of six northeastern states.

So, the other 3 boxes refer to students who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

The box you're referring to ("Not AS" and "Not NES") is for students who neither received a degree in the applied sciences not graduated from a school in one of six northeastern states.
This is just one of the boxes that meet the criteria of not both receiving a degree in the applied sciences and graduate from a school in one of six northeastern states.

Also, notice that the top-right box, also meets the criteria of not both receiving a degree in the applied sciences and graduate from a school in one of six northeastern states.

The bottom-left box also meets the criteria of not both receiving a degree in the applied sciences and graduate from a school in one of six northeastern states.

I hope that helps.

Cheers,
Brent
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by AndyMann » Sat Jun 22, 2013 12:12 pm
Awesome! Thanks for the explanations Mitch and Brent.

Brent,the concept is very nicely explained. Much appreciate. Thanks a lot!

Cheers,
Andy
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by nikhilgmat31 » Thu Oct 08, 2015 4:01 am
Mitch,
This statement in question seems very confusing.

"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"

Whether it says number of people who both didn't received applied science degree & nor graduated from NE states.

or
number of people who both didn't received applied science degree and people who are not graduated from NE states.
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by Zoser » Wed Feb 08, 2017 11:11 am
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.
Hi Brent!

As I understood, the question is asking for the fraction of the bottom right box (no Degree with No school). Can you explain why you included the three blue boxes and not just the bottom right?
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by Brent@GMATPrepNow » Wed Feb 08, 2017 11:33 am
Zoser wrote:
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.
Hi Brent!

As I understood, the question is asking for the fraction of the bottom right box (no Degree with No school). Can you explain why you included the three blue boxes and not just the bottom right?
The question is asking for more than just the number of students in the bottom right.

Here's the question: 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, the students in the top left box are those who BOTH received a degree in the applied sciences AND graduated from a school in one of six northeastern states.

So, the students in the remaining 3 boxes are those who did NOT BOTH receive a degree in the applied sciences AND graduate from a school in one of six northeastern states. This is the value that question is asking us to determine.

Does that help?

Cheers,
Brent
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by Zoser » Wed Feb 08, 2017 1:13 pm
Brent@GMATPrepNow wrote:
Zoser wrote:
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.
Hi Brent!

As I understood, the question is asking for the fraction of the bottom right box (no Degree with No school). Can you explain why you included the three blue boxes and not just the bottom right?
The question is asking for more than just the number of students in the bottom right.

Here's the question: 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, the students in the top left box are those who BOTH received a degree in the applied sciences AND graduated from a school in one of six northeastern states.

So, the students in the remaining 3 boxes are those who did NOT BOTH receive a degree in the applied sciences AND graduate from a school in one of six northeastern states. This is the value that question is asking us to determine.

Does that help?

Cheers,
Brent
I believe so. But if the question is asking for the bottom right box, how would it be probably be phrased?

Thanks
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by Matt@VeritasPrep » Fri Feb 17, 2017 2:06 am
Zoser wrote: I believe so. But if the question is asking for the bottom right box, how would it be probably be phrased?

Thanks
Zoser
"How many students neither received a degree in the applied sciences nor graduated from a school in one of six northeastern states?"
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by [email protected] » Fri Feb 17, 2017 10:37 am
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...
N = 12 graduates
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...

Final Answer: A

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

by fskilnik@GMATH » Thu Oct 18, 2018 12:27 pm
AndyMann 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
\[?\,\,\,:\,\,\,\# \,\,\,\,{\text{not}}\,\,\,\left[ {\,\,\left( {{\text{applied}}\,\,{\text{sciences}}\,\,{\text{degree}}} \right)\,\,{\text{AND}}\,\,\left( {{\text{in}}\,\,{\text{one}}\,\,{\text{of}}...} \right)\,\,} \right]\,\,\,\,\, = \,\,\,\,\# \,\,\,\left[ {\,\,\left( {{\text{not}}\,\,{\text{applied}}\,\,{\text{sciences}}\,\,{\text{degree}}} \right)\,\,{\text{OR}}\,\,\left( {{\text{not}}\,\,{\text{in}}\,\,{\text{one}}\,\,{\text{of}}...} \right)\,\,} \right]\,\]
\[N\,\,:\,\,{\text{graduated}}\,\,\,\, \to \,\,\,\,\left\{ \begin{gathered}
\,\frac{1}{3}N\,\,:\,\,{\text{applied}}\,\,{\text{sciences}}\,\,{\text{degree}}\,\,\,\, \to \,\,\,\,\left\{ \begin{gathered}
\,\frac{1}{4}\left( {\frac{1}{3}N} \right)\,\,\,:\,\,{\text{in}}\,{\text{one}}\,{\text{of}}\,\,... \hfill \\
\,\boxed{\frac{3}{4}\left( {\frac{1}{3}N} \right)}\,\,:\,\,{\text{not}}\,\,{\text{in}}\,\,{\text{one}}\,\,{\text{of}}\,\,... \hfill \\
\end{gathered} \right. \hfill \\
\,\boxed{\frac{2}{3}N}\,:\,\,{\text{not}}\,\,{\text{applied}}\,\,{\text{sciences}}\,\,{\text{degree}}\,\,\left( {{\text{and}}\,{\text{not}}\,\,{\text{in}}\,\,{\text{one}}\,\,{\text{of}}\,\,...} \right)\,\, \hfill \\
\end{gathered} \right.\]
\[?\,\,\mathop = \limits^{\left( * \right)} \,\,\,\frac{3}{4}\left( {\frac{1}{3}N} \right) + \frac{2}{3}N = \frac{{1 \cdot 3}}{{4 \cdot 3}}N + \frac{{2 \cdot 4}}{{3 \cdot 4}}N = \frac{{11}}{{12}}N\]
(*) 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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hi

by Scott@TargetTestPrep » Sun Apr 07, 2019 5:11 pm
AndyMann wrote:Will really appreciate if anyone can help to solve this question using Double set matrix method.

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

OA: A

Thanks a lot,
Andy
We see that N x 1/3 x 1/4 = N/12 people both received a degree in the applied sciences and graduated from a school in one of six northeastern states. Thus, 1 - N/12 = 11N/12 people did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states.

Note: The wording of this question is confusing. The question asks the number of people who DID NOT DO BOTH. If we let A = degree in applied science and N = graduated from a school in one of six northeastern states, then we see there are 4 possible events: [A,N] [A, not N] [not A, N] [not A, not N]. This question asks the number of people who were NOT [A, N], which means that we count the number of people in the three remaining events as the correct answer.

It is a common error to misinterpret the question as asking the number who were (only) [not A, not N], but in this case the question would be "How many people neither received a degree in applied science nor graduated from a school in one of six northeastern states.?

Answer: A

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