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# A total of 800 students were asked whether they found two

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A total of 800 students were asked whether they found two [#permalink]

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02 Aug 2012, 07:26
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----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500
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Re: A total of 800 students were asked whether they found two [#permalink]

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02 Aug 2012, 08:46
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Expert's post
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nobelgirl777 wrote:
----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

Since 200 students answered "yes" only for subject M, then the remaining 300 students who answered "yes" for subject M, also answered "yes" for subject R. So, 300 students answered "yes" for both subjects.

If 300 students answered "yes" for both subjects, then 400-300=100 students answered "yes" only for subject R.

So, we have that:
200 students answered "yes" only for subject M;
100 students answered "yes" only for subject R;
300 students answered "yes" for both subjects;

Therefore 800-(200+100+300)=200 students did not answer "yes" for either subject.

Hope it's clear.
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Re: A total of 800 students were asked whether they found two [#permalink]

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08 Aug 2012, 11:51
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Bunuel wrote:
nobelgirl777 wrote:
----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

Since 200 students answered "yes" only for subject M, then the remaining 300 students who answered "yes" for subject M, also answered "yes" for subject R. So, 300 students answered "yes" for both subjects.

If 300 students answered "yes" for both subjects, then 400-300=100 students answered "yes" only for subject R.

So, we have that:
200 students answered "yes" only for subject M;
100 students answered "yes" only for subject R;
300 students answered "yes" for both subjects;

Therefore 800-(200+100+300)=200 students did not answer "yes" for either subject.

Hope it's clear.

how did you deduce that the remaining 300 students must have said Yes to Subject R. There can be students who might have said Yes to Subject M and No to R and still be counted towards 500 who said Yes to M. Am I reading the premise wrongly?
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Re: A total of 800 students were asked whether they found two [#permalink]

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09 Aug 2012, 01:49
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inquisitive wrote:
Bunuel wrote:
nobelgirl777 wrote:
----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

Since 200 students answered "yes" only for subject M, then the remaining 300 students who answered "yes" for subject M, also answered "yes" for subject R. So, 300 students answered "yes" for both subjects.

If 300 students answered "yes" for both subjects, then 400-300=100 students answered "yes" only for subject R.

So, we have that:
200 students answered "yes" only for subject M;
100 students answered "yes" only for subject R;
300 students answered "yes" for both subjects;

Therefore 800-(200+100+300)=200 students did not answer "yes" for either subject.

Hope it's clear.

how did you deduce that the remaining 300 students must have said Yes to Subject R. There can be students who might have said Yes to Subject M and No to R and still be counted towards 500 who said Yes to M. Am I reading the premise wrongly?

Good question.

We know that 200 students answered YES only for subject M, so these 200 students answered something else for subject R. Now, what could have answered the remaining 300 students for subject R? If anyone of them answered either NO or UNSURE for subject R, then there would be more than 200 students who answered YES for only subject M. Therefore those 300 must have been answered YES for subject R.

Hope it's clear.
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Re: A total of 800 students were asked whether they found two [#permalink]

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09 Aug 2012, 04:54
Thank you Bunuel! I totally missed that. I hope these kind of questions dont appear on GMAT. but looks like this question is from GMAT prep. how common are these type of questions?
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Re: A total of 800 students were asked whether they found two [#permalink]

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09 Aug 2012, 04:57
inquisitive wrote:
Thank you Bunuel! I totally missed that. I hope these kind of questions dont appear on GMAT. but looks like this question is from GMAT prep. how common are these type of questions?

Data interpretation questions are quite common on quantitative section and even more common on integrated reasoning section of GMAT.
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Re: A total of 800 students were asked whether they found two [#permalink]

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09 Aug 2012, 22:06
Bunuel wrote:
inquisitive wrote:
Thank you Bunuel! I totally missed that. I hope these kind of questions dont appear on GMAT. but looks like this question is from GMAT prep. how common are these type of questions?

Data interpretation questions are quite common on quantitative section and even more common on integrated reasoning section of GMAT.

Hi Bunuel,
This was a wonderful problem. Could you share with a few more testing similar DI types Q's such as this one.
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Re: A total of 800 students were asked whether they found two [#permalink]

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19 Jan 2013, 20:57
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In this question a venn diagram approach would be easier don't you think? Easy to visualize.
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Re: A total of 800 students were asked whether they found two [#permalink]

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22 Apr 2013, 09:00
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This question just shows that how an easy concept can be enclosed in the hard shell of wordings
Sometimes the presentation of question can scare the test taker!
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Re: A total of 800 students were asked whether they found two [#permalink]

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23 May 2013, 07:46
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Total students = Yes Answers for M+ Yes answers for N - Yes intersection +Neither
800 = 500+400-300+Neither
Neither = 200

Consider kudos if my post helps!!!

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Re: A total of 800 students were asked whether they found two [#permalink]

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30 May 2013, 15:05
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For some reason, this problem is just not clicking for me. I don't understand why 300 said yes to both.
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Re: A total of 800 students were asked whether they found two [#permalink]

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31 May 2013, 01:23
aceon wrote:
For some reason, this problem is just not clicking for me. I don't understand why 300 said yes to both.

Explained here: a-total-of-800-students-were-asked-whether-they-found-two-136725.html#p1111575 Can you please tell me what part is unclear there, so to elaborate further? Thank you.
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Re: A total of 800 students were asked whether they found two [#permalink]

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01 Jun 2013, 03:38
nobelgirl777 wrote:
----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

Hope my approach is correct.

There are 200 students answered "yes" only for subject M, which means those 200 students said "no" or "unsure" for subject R. We know there are total of 400 students who said "no" or "unsure" for subject R.

400 - 200 = 200.

Hence, B.
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Re: A total of 800 students were asked whether they found two [#permalink]

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21 Jul 2013, 22:52
Bunuel wrote:
nobelgirl777 wrote:
----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

Since 200 students answered "yes" only for subject M, then the remaining 300 students who answered "yes" for subject M, also answered "yes" for subject R. So, 300 students answered "yes" for both subjects.

If 300 students answered "yes" for both subjects, then 400-300=100 students answered "yes" only for subject R.

So, we have that:
200 students answered "yes" only for subject M;
100 students answered "yes" only for subject R;
300 students answered "yes" for both subjects;

Therefore 800-(200+100+300)=200 students did not answer "yes" for either subject.

Hope it's clear.

Hi Bunnel,

how to do this problem fromt he point of view of "No's"
I mean how many responses were a NO for on M or R?

I made this table but got stuck:
M
Y N U
R Y 300 100 400
N 200 x? 100
U 300
500 200 100 800

Here can we say 100 said no only to M and 200 said no only to R?
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Re: A total of 800 students were asked whether they found two [#permalink]

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22 Jul 2013, 00:50
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1. There are 800 students and each should give responses on 2 subjects. So there are totally 1600 responses
2. Y(m) + Y(mr)=500 --- (i) Y(r) + Y(mr)=400 ---- (ii)
where Y(m) and Y(r) are the number of yes responses to M only and R only resp, and Y(mr) is the number of yes responses to both M and R..
3. Number of yes responses to M only is 200 i.e., Y(m) =200. Therefore from (i) Y(mr)=300
4. Also from (ii) Y(r)= 400-Y(mr) =100.
5. We have Y(m) + Y(mr) + Y(r) + Y(neither) = 800, as each student should fall into one of these
6. Therefore Y(neither) i.e., those who did not answer yes to either of the subjects is 200.
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Re: A total of 800 students were asked whether they found two [#permalink]

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06 Aug 2013, 21:29
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This can be solved easily with a venn diagram we are given for subject M yes only 200 and we can fill the other spots

The total is 800 = 200 + 100 + 300 + X

Neither Yes for both subject = 200
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venn.gif [ 11.91 KiB | Viewed 2055 times ]

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Re: A total of 800 students were asked whether they found two [#permalink]

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08 Oct 2013, 22:35
Bunuel wrote:
nobelgirl777 wrote:
----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

Since 200 students answered "yes" only for subject M, then the remaining 300 students who answered "yes" for subject M, also answered "yes" for subject R. So, 300 students answered "yes" for both subjects.

If 300 students answered "yes" for both subjects, then 400-300=100 students answered "yes" only for subject R.

So, we have that:
200 students answered "yes" only for subject M;
100 students answered "yes" only for subject R;
300 students answered "yes" for both subjects;

Therefore 800-(200+100+300)=200 students did not answer "yes" for either subject.

Hope it's clear.

I am unable to understand the question and solution, is it GMAT qn?
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Re: A total of 800 students were asked whether they found two [#permalink]

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09 Oct 2013, 01:29
honchos wrote:
Bunuel wrote:
nobelgirl777 wrote:
----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500

Since 200 students answered "yes" only for subject M, then the remaining 300 students who answered "yes" for subject M, also answered "yes" for subject R. So, 300 students answered "yes" for both subjects.

If 300 students answered "yes" for both subjects, then 400-300=100 students answered "yes" only for subject R.

So, we have that:
200 students answered "yes" only for subject M;
100 students answered "yes" only for subject R;
300 students answered "yes" for both subjects;

Therefore 800-(200+100+300)=200 students did not answer "yes" for either subject.

Hope it's clear.

I am unable to understand the question and solution, is it GMAT qn?

Yes. It's a GMAT question. As for the solution: please elaborate what exactly didn't you understand.
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Re: A total of 800 students were asked whether they found two [#permalink]

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23 Oct 2013, 22:48
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For people that are having a hard time understand this question, hopefully this table will help:

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Re: A total of 800 students were asked whether they found two [#permalink]

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03 Jun 2014, 08:31
saintforlife wrote:
For people that are having a hard time understand this question, hopefully this table will help:

Hi, There is a typo in your table. The total no. of students who did not say yes to M should be 300. Thanks!
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Re: A total of 800 students were asked whether they found two   [#permalink] 03 Jun 2014, 08:31

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