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Last year, there were 3 sections in the Catalyst, a mock CAT paper. Out of them 33  students cleared the cut-off in Section 1, 34 students cleared the cut-off in Section 2 and 32 cleared the cut-off in Section 3. 10 students cleared the cut-off in Section 1 and Section 2, 9 cleared the cut-off in Section 2 and Section 3, 8 cleared the cut-off in Section 1 and Section 3. The numberof people who cleared each section alone wasequal and was 21 for each section.
How many cleared only one of the three sections ?
  • a)
    21
  • b)
    63
  • c)
    42
  • d)
    52
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Last year, there were 3 sections in the Catalyst, a mock CAT paper. Ou...
21 + 21 +21 = 63
Option (B) is correct
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Most Upvoted Answer
Last year, there were 3 sections in the Catalyst, a mock CAT paper. Ou...
Given Information:
- 33 students cleared the cut-off in Section 1.
- 34 students cleared the cut-off in Section 2.
- 32 students cleared the cut-off in Section 3.
- 10 students cleared the cut-off in Section 1 and Section 2.
- 9 students cleared the cut-off in Section 2 and Section 3.
- 8 students cleared the cut-off in Section 1 and Section 3.
- The number of people who cleared each section alone was equal and was 21 for each section.

To Find: The number of students who cleared only one of the three sections.

Solution:
Let the number of students who cleared all three sections be x.
From the given information, we can form the following equations:
- Number of students who cleared Section 1 = x + 8 + 10 + 21 = x + 39
- Number of students who cleared Section 2 = x + 10 + 9 + 21 = x + 40
- Number of students who cleared Section 3 = x + 9 + 8 + 21 = x + 38
- Number of students who cleared exactly one section = 21 * 3 = 63

Now, we can find the value of x by adding the number of students who cleared each section and subtracting the students who cleared more than one section:
Total number of students = 33 + 34 + 32 - (10 + 9 + 8) + x
Total number of students = 72 + x
Therefore, x = Total number of students - 72

Substituting this value of x in the above equations, we get:
- Number of students who cleared Section 1 = Total number of students - 33
- Number of students who cleared Section 2 = Total number of students - 32
- Number of students who cleared Section 3 = Total number of students - 34

Now, to find the number of students who cleared only one section, we can use the formula:
Number of students who cleared exactly one section = Total number of students - (Number of students who cleared more than one section) - (Number of students who cleared no section)

Number of students who cleared no section = Total number of students - (Number of students who cleared at least one section)
Number of students who cleared at least one section = Number of students who cleared Section 1 + Number of students who cleared Section 2 + Number of students who cleared Section 3 - (Number of students who cleared exactly two sections) - 2*(Number of students who cleared all three sections)

Number of students who cleared exactly two sections = (10 + 9 + 8) = 27
Number of students who cleared all three sections = x = Total number of students - 72

Substituting the given values, we get:
Number of students who cleared at least one section = (Total number of students - 33) + (Total number of students - 32) + (Total number of students - 34) - 27 - 2*(Total number of students - 72)
Number of students who cleared at least one section = 3*Total number of students - 198

Number of students who cleared no section = Total number of students - (3*Total number of students - 198)
Number of students who cleared no section = 198
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Last year, there were 3 sections in the Catalyst, a mock CAT paper. Out of them 33 students cleared the cut-off in Section 1, 34 students cleared the cut-off in Section 2 and 32 cleared the cut-off in Section 3. 10 students cleared the cut-off in Section 1 and Section 2, 9 cleared the cut-off in Section 2 and Section 3, 8 cleared the cut-off in Section 1 and Section 3. The numberof people who cleared each section alone wasequal and was 21 for each section.How many cleared only one of the three sections ?a)21b)63c)42d)52Correct answer is option 'B'. Can you explain this answer?
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