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

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

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03 Jun 2014, 22:12
fozzzy wrote:
In this question a venn diagram approach would be easier don't you think? Easy to visualize.

I usually try to attempt such questions using Venn diagram, but was unable to do

Can anyone try doing this using Venn Diagram? Thanks in advance
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Re: A total of 800 students were asked whether they found two subjects, M [#permalink]

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01 Aug 2014, 23:08
Hello,

I solved it this way.

Given: 200 students answered YES only for sub M. also from given table, total number of students, who answered YES to sub M = 500.
this implies, 500-200=300 students who answered YES to both sub M & sub R. => {MnR}

now i am applying sets formula of {M U R} = {M} + {R} - {MnR} = 500 + 400 - 300 = 600.
And ans to our que = Total - {M U R} = 800 - 600 = 200, are number of studs who didnt ans YES for either sub.

hope this helps too.

Thanks.

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

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22 Nov 2014, 03:34
GMATBaumgartner wrote:
Hi Bunuel,
This was a wonderful problem. Could you share with a few more testing similar DI types Q's such as this one.

Hi Bunuel!

Do we have more questions of this type? Kindly share links
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Re: A total of 800 students were asked whether they found two subjects, M [#permalink]

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22 Nov 2014, 03:44
PareshGmat wrote:
fozzzy wrote:
In this question a venn diagram approach would be easier don't you think? Easy to visualize.

I usually try to attempt such questions using Venn diagram, but was unable to do

Can anyone try doing this using Venn Diagram? Thanks in advance

Here is a Venn Diagram attempt! Read it thus:
R ==> Yes only for R
B ==> Yes for both
S ==> Yes only for M (sorry typo )
Attachment:

Untitled.png [ 11.46 KiB | Viewed 1404 times ]

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

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06 Dec 2014, 09:40
wow, i'm glad i come to the forums. this is 50 times faster than the explanation gmatprep provided.

it should be illegal - their solutions!

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.

Answer: B.

Hope it's clear.

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

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31 Mar 2015, 10:53
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

Given that 200 students answered YES only for subject M.
There are 500-200 = 300 more students who answered YES for subject M.
So, remaining 300 students who answered YES for subject M, also answered YES for subject R.
Hence, 300 students answered YES for both subjects.
This implies that 400-300 = 100 students answered YES only for subject R.

So, 800-(200+100+300)=200 students did NOT answer YES for either subject.

Hence option (B).

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

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31 Mar 2015, 13:17
I've made it very quickly (few seconds) but correct me if i'm wrong :

200 who "yes" on M -> voted "no" or "unsure" for R...
As a consequence, the 400 who voted "yes" on R are different from the 200 above.

Then the sum of the student's who said yes for either M or R is 600 (400 + 200 ).

Then those who never said yes to anything are 800 - 600 = 200.

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

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16 Aug 2015, 22:13
In case, we are not able to solve the question, we can atleast eliminate few options -
since Yes for Subject M is 500, the number of students who did not answer Yes to either subjects can be max (800 (total students) minus 500). i.e. max 300.Eliminate D and E.

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

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09 Nov 2015, 17:46
I am pretty impressed with the official solution in the GMATprep, which uses 6 equations and a big table to solve this problem! Why they do this?? While this problem is not easy the solution is quite simple: if 200 like only M and the table says that 500 like M in general, then it must be that 300 like M and R. So if 300 like M and R and the table says that 400 like R in general, then it must be that 100 like only R. Since there are 800 students and 200 (only M)+ 100 (only R) + 300 (M and R)= 600 like M or R then 800-600=200 don't like either subject.

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

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22 Nov 2015, 23:13
i cant figure out how does the "unsure" part affect the venn/matrix? kudos in advance
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Re: A total of 800 students were asked whether they found two subjects, M [#permalink]

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23 Nov 2015, 03:34
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shasadou wrote:
i cant figure out how does the "unsure" part affect the venn/matrix? kudos in advance

Considering what the question is asking, it would be useful to consider only the following sets: people that found M interesting, people that do not found M interesting;people that found R interesting, people that do not found R interesting. Using this line of reasoning, the "Unsure" is included in the "do not found interesting", e.g. people that do not found M interesting = 200+100=300. I can tell you that the unsure is to confuse us; it is put to make the question harder.

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

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16 Jul 2016, 08:17
I'm usually good with Overlapping sets.. however this problem is completely throwing me off...
Looks like we are completely ignoring 'unsure'?
If 500 said Yes to M, but prompt says 200 said Yes to ONLY M.. means 300 said yes to Both M and R. But since prompt says 400 said yes to R, means 100 said yes to ONLY R... I got that far. How do I proceed to find out the # of students who did not answer YES for either? Do I set up a table now and ignore the unsure completely since the prompt isn't really asking about unsures?
------- M (yes):: M (no):: Total
R (yes):: ____ :: 100 :: 400
R (no):: 200 :: _____ :: ____
Total :: 500 :: _____ :: 800
... and then fill out the empty areas and you get ans: 200...

Is this way correct? I'm still not 100% confident I understand this problem..
Thanks in advance!

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

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23 Sep 2016, 11:14
My two cents...

The test just put extra info to make it more difficult. It is pretty simple.
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Re: A total of 800 students were asked whether they found two subjects, M [#permalink]

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29 Dec 2016, 03:49
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.

Answer: B.

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?

for the 500 who said yes to M of which 200 said yes to M only. if the other 300 said yes to M and no or unsure for R , thus those 300 said yes to M only which is not the case

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

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07 Jan 2017, 06:10
Using the 2-set formula on the first column:

Total = (YES4M) + (YES4R) - Both + Neither

Total = 800

(YES4M) = 500

(YES4R) = 400

Actually, the text already gives you (YES4M) - Both = 200, which means "200 students answered "yes" only for subject M"

So we are left with "Neither" unknown:

800 = 200 + 400 + Neither ---> Neither = 200

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

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04 Apr 2017, 00:52
Why is it all about the YES column while instead the NO and UNSURE are ignored in the calculation ?

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

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16 Apr 2017, 10:57
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This is another solution to this GMAT question. I hope it helps.
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Re: A total of 800 students were asked whether they found two subjects, M [#permalink]

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01 Jul 2017, 03:58
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.

Answer: B.

Hope it's clear.

If I build a Venn diagram for M, R and both only for Yes section. Then I get that 800= 500+400-300 + Neither

So, Neither = 800-600=200.

These students said neither yes for Subject M nor subject R.

Is there any trick in the question which inhibits using Venn diagram (I am considering only the Yes scenario) for this situation since the level is 700+?

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

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22 Jul 2017, 09:48
I think the difficult part of this problem is organizing the information. The question gives you three different categories for answers and two different groups, which is a deviation from the normal overlapping sets problems that give you either three groups with overlap or two groups that overlap on two different binary factors.

However, notice that the question asks you about "YES" and (essentially) "NOT YES". This means that you can treat this like an overlapping set question in a 2x2 matrix (as has been described above).

If we re-write the matrix in the question for just "YES" and "NOT YES" and the two subjects, it looks like this:

YES NOT YES
Subject M 500 300
Subject R 400 400

We want to find the people who didn't vote yes for either category. More specifically, we want:

Total = (Yes for M) + (Yes for R) - (Yes for BOTH) + NEITHER

NEITHER is what we are looking for and we are given (Yes for M) and (Yes for R) and we need to find (Yes for BOTH) then we will have one variable to solve for. So how many people are in the (Yes for BOTH) category?

Ok so then the question tells you that 200 people answered YES for only Subject M. That means there must be (500-200) = 300 people who voted yes for both of them and so are getting double-counted (I think fozzzy's venn diagram shows this pretty well).

Aside: As others have mentioned you can also use this information to find out how many people voted YES for just Subject R (if that was the question). That figure would be 100.

However, we can now solve for the variable we are looking for:

Total = (Yes for M) + (Yes for R) - (Yes for BOTH) + NEITHER
800 = 500 + 400 - 300 + NEITHER
200 = NEITHER

(B)

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A total of 800 students were asked whether they found two subjects, M   [#permalink] 22 Jul 2017, 09:48

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

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