The annual sports meet of Don Bosco School spanned three days. The following facts are known about the number of participating students.1. It is compulsory for every student to participate in at least one sport.2. Number of students participating on day 1 and 3 was 80 and 75 respectively. 20 students played on all three days.3. Number of students participating on both day 1 and day 2 was equal to those who played on both day 2 and day 3 and also those who played on both day 1 and day 3.4. 65 students participated on more than one day.If there were 150 students in the school, how many students played on Day 2?Correct answer is '80'. Can you explain this answer?

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The annual sports meet of Don Bosco School spanned three days. The following facts are known about the number of participating students.
1. It is compulsory for every student to participate in at least one sport.
2. Number of students participating on day 1 and 3 was 80 and 75 respectively. 20 students played on all three days.
3. Number of students participating on both day 1 and day 2 was equal to those who played on both day 2 and day 3 and also those who played on both day 1 and day 3.
4. 65 students participated on more than one day.
If there were 150 students in the school, how many students played on Day 2?

Correct answer is '80'. Can you explain this answer?

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The annual sports meet of Don Bosco School spanned three days. The fol...

By the data given in the question we can draw the following venn diagram.

From (3), a = b = c Also,
from (2) and (4), a + b + c + 20 = 65
a = b = c = 15
Number of students who participated on day 1 only = 30 Number of students who participated on day 3 only = 25
Let the number of students who participated on day 2 only be y.
Filling data in the venn diagram we get,

Total number of students in the school = 30 + 25 + 15 + 15 + 15 + 20 + y
150 = 120 + y
y = 30
Number of students who participated on day 2 = 20 + 30 + 30 = 80
Answer: 80

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The annual sports meet of Don Bosco School spanned three days. The fol...

Given Information:
- Number of students participating on day 1 = 80
- Number of students participating on day 3 = 75
- Number of students playing on all three days = 20
- Number of students participating on both day 1 and day 2 = Number of students participating on both day 2 and day 3 = Number of students participating on both day 1 and day 3
- Number of students participating on more than one day = 65

Assumptions:
- All students in the school participate in at least one sport.
- There are no students who only participate on day 2.

Let's solve the problem step by step:

Step 1: Find the total number of students participating on day 1, day 2, and day 3.

- Number of students participating on day 1 = 80
- Number of students participating on day 3 = 75
- Number of students playing on all three days = 20

Total number of students participating on day 1 or day 3:
= Number of students participating on day 1 + Number of students participating on day 3 - Number of students playing on all three days
= 80 + 75 - 20
= 135

Step 2: Find the number of students participating on both day 1 and day 2.

- Number of students participating on both day 1 and day 2 = Number of students participating on both day 2 and day 3 = Number of students participating on both day 1 and day 3 (given)

Let's assume the number of students participating on both day 1 and day 2 as x.

- Number of students participating on day 1 only = 80 - x
- Number of students participating on day 2 only = x
- Number of students participating on day 3 only = 75 - x

Total number of students participating on day 1 or day 2:
= Number of students participating on day 1 only + Number of students participating on day 2 only + Number of students participating on both day 1 and day 2
= 80 - x + x + x
= 80 + x

Total number of students participating on day 2 or day 3:
= Number of students participating on day 2 only + Number of students participating on day 3 only + Number of students participating on both day 1 and day 2
= x + 75 - x + x
= 75 + x

From the given information, we know that the number of students participating on more than one day = 65.

Step 3: Set up an equation using the information from Step 2.

Total number of students participating on day 1 or day 2 or day 3:
= Total number of students participating on day 1 or day 2 + Total number of students participating on day 2 or day 3 - Number of students playing on all three days + Number of students participating on both day 1 and day 2
= 80 + x + 75 + x - 20 + x

Since the total number of students in the school is 150, we can set up the following equation:

Answered by Wizius Careers · View profile

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The annual sports meet of Don Bosco School spanned three days. The following facts are known about the number of participating students.1. It is compulsory for every student to participate in at least one sport.2. Number of students participating on day 1 and 3 was 80 and 75 respectively. 20 students played on all three days.3. Number of students participating on both day 1 and day 2 was equal to those who played on both day 2 and day 3 and also those who played on both day 1 and day 3.4. 65 students participated on more than one day.If there were 150 students in the school, how many students played on Day 2?Correct answer is '80'. Can you explain this answer?

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The annual sports meet of Don Bosco School spanned three days. The following facts are known about the number of participating students.1. It is compulsory for every student to participate in at least one sport.2. Number of students participating on day 1 and 3 was 80 and 75 respectively. 20 students played on all three days.3. Number of students participating on both day 1 and day 2 was equal to those who played on both day 2 and day 3 and also those who played on both day 1 and day 3.4. 65 students participated on more than one day.If there were 150 students in the school, how many students played on Day 2?Correct answer is '80'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The annual sports meet of Don Bosco School spanned three days. The following facts are known about the number of participating students.1. It is compulsory for every student to participate in at least one sport.2. Number of students participating on day 1 and 3 was 80 and 75 respectively. 20 students played on all three days.3. Number of students participating on both day 1 and day 2 was equal to those who played on both day 2 and day 3 and also those who played on both day 1 and day 3.4. 65 students participated on more than one day.If there were 150 students in the school, how many students played on Day 2?Correct answer is '80'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The annual sports meet of Don Bosco School spanned three days. The following facts are known about the number of participating students.1. It is compulsory for every student to participate in at least one sport.2. Number of students participating on day 1 and 3 was 80 and 75 respectively. 20 students played on all three days.3. Number of students participating on both day 1 and day 2 was equal to those who played on both day 2 and day 3 and also those who played on both day 1 and day 3.4. 65 students participated on more than one day.If there were 150 students in the school, how many students played on Day 2?Correct answer is '80'. Can you explain this answer?.

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