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: - 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)
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 = 200Correct Answer: Choice B Best,
Aditi Gupta
Quant expert,
e-GMAT _________________