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In a mock exam, there were 3 sections. Out of all students, 60 students cleared the cut off in section 1, 50 students cleared the cutoff in section 2 and 56 students cleared the cut off in section 3. 20 students cleared the cutoff in section 1 and section 2, 16 cleared cut off in section 2 & section 3, 26 cleared the cut off in section 1 & section 3. The number of students who cleared cutoff of the only one section was equal & was 24 for each section. How many students cleared cut off all the three sections?
  • a)
    6
  • b)
    8
  • c)
    10
  • d)
    12
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a mock exam, there were 3 sections. Out of all students, 60 student...
Let the number of students be X who cleared cut off in all sections.
The number of students who cleared the cutoff in section 1 and section 2, only = 20 – X
The number of students who cleared the cutoff in section 2 and section 3, only = 16 – X
The number of students who cleared the cutoff in section 1 and section 3, only = 26 – X
Now, consider section 1:
24 + 20 – x + x + 26 – x = 60
70 – x = 60
x = 10
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Most Upvoted Answer
In a mock exam, there were 3 sections. Out of all students, 60 student...
And section 3, and 12 cleared the cut off in section 1 and section 3.

To find the number of students who cleared the cut off in all three sections, we can use the principle of inclusion-exclusion.

Let's denote the number of students who cleared the cut off in section 1, section 2, and section 3 as A, B, and C respectively.

We know that A = 60, B = 50, and C = 56.

We also know that 20 students cleared the cutoff in section 1 and section 2, 16 cleared the cutoff in section 2 and section 3, and 12 cleared the cutoff in section 1 and section 3.

Let's denote the number of students who cleared the cut off in both section 1 and section 2 as X, in both section 2 and section 3 as Y, and in both section 1 and section 3 as Z.

We want to find the number of students who cleared the cut off in all three sections, which we can denote as N.

Using the principle of inclusion-exclusion, we can write:

N = A + B + C - (X + Y + Z)

We know that A = 60, B = 50, C = 56, X = 20, Y = 16, and Z = 12.

Substituting these values into the equation, we get:

N = 60 + 50 + 56 - (20 + 16 + 12)

N = 166 - 48

N = 118

Therefore, the number of students who cleared the cut off in all three sections is 118.
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In a mock exam, there were 3 sections. Out of all students, 60 students cleared the cut off in section 1, 50 students cleared the cutoff in section 2 and 56 students cleared the cut off in section 3. 20 students cleared the cutoff in section 1 and section 2, 16 cleared cut off in section 2 & section 3, 26 cleared the cut off in section 1 & section 3. The number of students who cleared cutoff of the only one section was equal & was 24 for each section. How many students cleared cut off all the three sections?a)6b)8c)10d)12Correct answer is option 'C'. Can you explain this answer?
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