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CAT Exam  >  CAT Questions  >  200 students appeared in a specific examinati... Start Learning for Free
200 students appeared in a specific examination.
There were 80 students who failed in Mathematics.
160 students passed in Physics.
30 students failed in Chemistry.
30 students failed in Mathematics and Physics.
15 students failed in Mathematics and Chemistry.
10 students failed in Physics and Chemistry.
100 students passed in all three subjects.
Q. How many students failed in only one subject?
  • a)
    45
  • b)
    55
  • c)
    30
  • d)
    80
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
200 students appeared in a specific examination.There were 80 students...
Given data:
Total number of students = 200
Number of students who failed in Mathematics = 80
Number of students who passed in Physics = 160
Number of students who failed in Chemistry = 30
Number of students who failed in Mathematics and Physics = 30
Number of students who failed in Mathematics and Chemistry = 15
Number of students who failed in Physics and Chemistry = 10
Number of students who passed in all three subjects = 100

To find: Number of students who failed in only one subject

Approach:
To find the number of students who failed in only one subject, we need to subtract the number of students who failed in two or three subjects from the total number of students who failed.

Let us first find the number of students who failed in two or three subjects:
Number of students who failed in Mathematics and Physics = 30
Number of students who failed in Mathematics and Chemistry = 15
Number of students who failed in Physics and Chemistry = 10
Number of students who failed in all three subjects = Total number of students - Number of students who passed in all three subjects
= 200 - 100
= 100

Therefore, the number of students who failed in two or three subjects = 30 + 15 + 10 + 100 = 155

Now, the number of students who failed in only one subject = Total number of students who failed - Number of students who failed in two or three subjects
= 80 - 155 (as 155 is greater than 80, we can take the absolute value of the difference)
= |80 - 155|
= 75

Hence, the number of students who failed in only one subject is 75, which is option (B).
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Community Answer
200 students appeared in a specific examination.There were 80 students...
Concept used:
The Venn diagram is constructed based on the number of students who failed the exam.
Calculation:
From the given information we get,
C + D + G + F = 30
G + E = 30
G + F = 15
D + G = 10
B + E + G + F = 80
From the data we can deduce the following:
A + E + G + D = 200 - 160 = 40
C + A + D = 20
A + E + B = 70
B + F + C = 60
Substituting and solving we get,
A = 5, B = 40,  E = 25, G = 5, F = 10, C = 10, D = 5
Number of people who failed in only one subject = A + B + C = 5 + 40 + 10 = 55 
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200 students appeared in a specific examination.There were 80 students who failed in Mathematics.160 students passed in Physics.30 students failed in Chemistry.30 students failed in Mathematics and Physics.15 students failed in Mathematics and Chemistry.10 students failed in Physics and Chemistry.100 students passed in all three subjects.Q. How many students failed in only one subject?a)45b)55c)30d)80Correct answer is option 'B'. Can you explain this answer?
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