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

Question

https://gmatclub.com/forum/download/file.php?id=73212 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 PS01452 2023-11-08_19-26-37.png

Bunuel · Accepted Answer

----------------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

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.

Bunuel · Answer

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.

inquisitive · Answer

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?

Archit143 · Answer

----------------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

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

Total students = Yes Answers for M+ Yes answers for N - Yes intersection +Neither
800 = 500+400-300+Neither
Neither = 200

Archit

SVaidyaraman · Answer

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.

fozzzy · Answer

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

saintforlife · Answer

For people that are having a hard time understand this question, hopefully this table will help:

https://i.imgur.com/jgfAGav.png

NoHalfMeasures · Answer

Hi, There is a typo in your table. The total no. of students who did not say yes to M should be 300. Thanks!

OptimusPrepJanielle · Answer

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). -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

chanlex · Answer

This is another solution to this GMAT question. I hope it helps.

grassmonkey · Answer

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)

ScottTargetTestPrep · Answer

Since 200 students answered "yes" for only subject M, the remaining 300 students who answered “yes” for subject M must also have answered “yes” for subject R. That means only 100 students answer “yes” for only subject R. In other words, the total number of students who answered “yes” to one or both subjects is 200 + 300 + 100 = 600, which means 800 - 600 = 200 students did not answer “yes” for either subject.

Answer: B

BrentGMATPrepNow · Answer

Another approach is to use the   Double Matrix Method  . This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). 
Here, we have a population of students, and the two characteristics are: 
- Said "yes" to liking subject M or didn't say "yes" to liking subject M
- Said "yes" to liking subject R or didn't say "yes" to liking subject R

IMPORTANT: Notice that I just lumped the "unsure" respondents in with those who answered "no." It's okay to do this since the question is only interested in those who did not answer "yes" 
So, we can CONDENSE our table to get: 
 Subject M: 500 answered "yes," and 300 did NOT answer "yes" 
Subject R: 400 answered "yes," and 400 did NOT answer "yes"

We can now set up our diagram as follows:
 https://i.imgur.com/uuRupkQ.png

The question tells us   200 students answered "yes" only for subject M  
So, we know that 200 students can be placed in the bottom-left box:
 https://i.imgur.com/4SGUV1f.png

From here, we can find the other values in the empty boxes: 
 https://i.imgur.com/KNf1N9h.png

The question asks:   How many of the students did not answer "yes" for either subject?   
The bottom-right box represents those students:
 https://i.imgur.com/pCCMB3D.png

So, the correct answer is B

This question type is  VERY COMMON  on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:
 https://www.youtube.com/watch?v=jK-tiBrrf04

EXTRA PRACTICE QUESTION
 https://www.youtube.com/watch?v=DsbPUSH_Wu4

Kinshook · Answer

----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300

Given: 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.

Asked: If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

If 200 students answered "Yes" only for subject M, then 500-200=300 students answered "Yes" for both subjects and 400-300=100 students answered "Yes" only for subject R.

Number of students who did not answer "Yes" to any subject = 800 - 200 - 100 - 300 = 200 students

IMO B

mcelroytutoring · Answer

Attached is a visual that should help.

egmat · Answer

GIVEN:    
  A total of 800 students responded to a survey about their interest in two subjects – M and R. 
  For each subject, each respondent answered with a “Yes”, “No” or “Unsure”.   
 200 students answered “yes”  only  for subject M.

TO FIND:    
  Number of students who DID NOT answer “Yes” for either subject.

Let’s first understand what exactly the asked question means. Once you’re clear with this, the final working out will be straightforward.

UNDERSTAND THE QUESTION:    
We want the number of students who  did NOT answer “Yes” to either subject.  To understand this clearly, let’s break the statement into two small pieces.

Part 1:  
First, we’ll understand what it means when we say a student does NOT answer “Yes” to a subject. Well, not answering “Yes” means answering either “No” or “Unsure” – that is everything  except  “Yes”. 
For any subject, we can find these people by subtracting those who did say “Yes” from the total people who responded, that is, from 800. 
   Subject M:  #Students  not  answering “Yes” for subject M 
  =  800 - #students answering “Yes” to M    
  Subject R:  #Students  not  answering “Yes” for subject R 
  =  800 - #students answering “Yes” to R

Part 2:  
Next, we need to understand that “not saying yes to either” means “not saying yes to ANY of M and R- not a yes to M and not a yes to R.” 
So, if we combine everything above, we get that our required number is: 
 800 – (# of students who answered “Yes” to M or R) ----(I)

WORKING OUT:    
From (I), we understood that to answer our question, we need to find the #students who answer “Yes” to M or R. 
Now, since there are chances of some students having said “Yes” to both subjects, the #students who said “Yes” to either M or R is  NOT  just the sum of those who said “yes” to M and those who said “yes” to R. 
The correct formula to calculate the #students who answered  “Yes” to M or R  is: 
  (#Answered “Yes” to M)  UNION  (#Answered “Yes” to R).

To comfortably find this value, let’s visualize the situation on a Venn diagram.

Venn Diagram:  
We already know the following from the given information: 
  #Students who answered “Yes” to  M  = 500 
 #Students who answered “Yes” to  R  = 400 
 #Students who answered “Yes” to  ONLY M  = 200 ----(II)

https://i.imgur.com/dApqpwd.png 
Here, ‘x’, ‘y’ and ‘z’ represent those who answered “Yes” to only M, to both M and R, and to only R, respectively. 
So, from (II), we can say that x = 200, x + y = 500, and y + z = 400. 
Solving, we get y = 300 and z = 100.

So, the number of students who answered “Yes” to either of the subjects, that is, (Yes to M)  UNION  (Yes to R) is given by x + y + z. 
 - So, x + y + z = 200 + 300 + 100 = 600

Using (I),  the required answer  =  800 – 600 = 200

Correct Answer:   Choice B

Best, 
Aditi Gupta 
Quant expert, e-GMAT

DanTheGMATMan · Answer

Keep it simple. It's just yes and "not yes" for each. They do this kind of thing all the time:

https://www.youtube.com/watch?v=TE4QZ3c0lcs

SudsMeister · Answer

If identifying the common part where students answered "Yes" for both M and N is a bit confusing to decipher - as it was for me, then an alternative way that worked for me is: Image 1.jpg We want to find number of students that did not answer "Yes" for M or N = Yellow area in the image = 800 - number of students who answered "Yes" for M or N = 800 - (Red area in image + area inside blue circle) We are given: Number of students that answered "Yes" only for M = Red area in image = 200 Number of students that answered "Yes" for N = Area inside blue circle = 400 Yellow area = 800 - Red area - area inside blue circle = 800 - 200 - 400 = 200. Answer B. Note: When we are given total students who answered "Yes" for N, that count includes all the students who answered "Yes" only for N + all the students who answered "Yes" for both M and N. So, we need not calculate the figure "Yes" for both M and N separately.

siddhantvarma · Answer

KarishmaB  is there any significance of the information in the two remaining columns "No" and "Unsure" since we don't need that data to get to the answer?

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

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