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A test was conducted in three sections X,Y,Z of tenth class. The average marks per student of sections X and Y together is 66. The average marks per student of sections Y and Z together is 63. The average marks per student of sections Z and X together is 67. The average marks per student of the three sections together is A. Find the number of integral values that A can take?
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Most Upvoted Answer
A test was conducted in three sections X,Y,Z of tenth class. The avera...
Answer is zero.
Here, (x+y)/2=66; (y+z)/2=63; (z+x)/2=67
so, 2*(x+y+z)=2*(66+63+67)
or x+y+z=196
in question it is asked that,
(x+y+z)/3=?
so, 196/3=65.333=A;
that means no integral values for A.
Community Answer
A test was conducted in three sections X,Y,Z of tenth class. The avera...
Problem: A test was conducted in three sections X,Y,Z of tenth class. The average marks per student of sections X and Y together is 66. The average marks per student of sections Y and Z together is 63. The average marks per student of sections Z and X together is 67. The average marks per student of the three sections together is A. Find the number of integral values that A can take?

Solution:

Step 1: Understanding the problem

- Three sections X, Y, Z of tenth class
- Average marks per student of X and Y = 66
- Average marks per student of Y and Z = 63
- Average marks per student of Z and X = 67
- Average marks per student of all three sections = A
- We need to find the number of integral values that A can take

Step 2: Expressing the problem mathematically

Let the number of students in sections X, Y, and Z be x, y, and z respectively.

- Total marks in section X + Total marks in section Y = (66)(x+y)
- Total marks in section Y + Total marks in section Z = (63)(y+z)
- Total marks in section Z + Total marks in section X = (67)(z+x)
- Total marks in all three sections = Ax + Ay + Az

We can simplify the above equations to get:

- 66x + 66y = 132(x+y) = Total marks in section X and Y
- 63y + 63z = 126(y+z) = Total marks in section Y and Z
- 67z + 67x = 134(z+x) = Total marks in section Z and X
- (Ax + Ay + Az)/(x+y+z) = A = Average marks per student of all three sections

Step 3: Simplifying the equations

We can simplify the above equations as follows:

- 66x - 66y = 0
- 63y - 63z = 0
- 67z - 67x = 0

We can solve the above equations to get:

- x = y
- y = z
- z = x

Therefore, the number of students in each section is the same.

Step 4: Finding the number of integral values that A can take

Let the number of students in each section be n.

- Total marks in section X + Total marks in section Y = 66n(n+n) = 132n^2
- Total marks in section Y + Total marks in section Z = 63n(2n) = 126n^2
- Total marks in section Z + Total marks in section X = 67n(2n) = 134n^2
- Total marks in all three sections = A(3n^2)

Adding the above equations, we get:

Total marks in all three sections = 392n^2

Therefore, A = (392n^2)/(3n^2) = (392/3)

A can take only one integral value, which is 130.

Step 5: Conclusion

- The average marks per student of all three sections can take only one integral value, which is
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Directions: In a school, for class 10th the sections are allotted on the basis of the scores of the student in class 9th. There are four sections in class 9th namely A, B, C, D. A student obtaining highest marks will be allotted section P in class 10th. On the similar basis sections Q, R, S are allotted. P is the best section, Q, R and S are the 2nd, 3rd and 4th best section respectively.A record of score of 10 students were kept.Each year the lowest and highest score increases by 1.Each student got distinct marks as per record of January, 2011, the minimum marks is 20 and the maximum marks is 29. The sections were to be continued for 1 year in class 10th. Different sets of number of students are there in class 9th for any two year. In class 10th, section P has 4 students and, Q, R, S have 2 students each.The below table gives the number of students in each section of class 9th over the years:Q. Total number of students from section C moved in section Q in the year 2011 is what was the highest marks obtained by the student of section B in the year 2013?

Directions: In a school, for class 10th the sections are allotted on the basis of the scores of the student in class 9th. There are four sections in class 9th namely A, B, C, D. A student obtaining highest marks will be allotted section P in class 10th. On the similar basis sections Q, R, S are allotted. P is the best section, Q, R and S are the 2nd, 3rd and 4th best section respectively.A record of score of 10 students were kept.Each year the lowest and highest score increases by 1.Each student got distinct marks as per record of January, 2011, the minimum marks is 20 and the maximum marks is 29. The sections were to be continued for 1 year in class 10th. Different sets of number of students are there in class 9th for any two year. In class 10th, section P has 4 students and, Q, R, S have 2 students each.The below table gives the number of students in each section of class 9th over the years:Q. What was the highest marks obtained by the student of section B in the year 2013?

Directions : In a school, for class 10th the sections are allotted on the basis of the scores of the student in class 9th. There are four sections in class 9th namely A, B, C, D. A student obtaining highest marks will be allotted section P in class 10th. On the similar basis sections Q, R, S are allotted. P is the best section, Q, R and S are the 2nd, 3rd and 4th best section respectively.A record of score of 10 students were kept.Each year the lowest and highest score increases by 1.Each student got distinct marks as per record of January, 2011, the minimum marks is 20 and the maximum marks is 29. The sections were to be continued for 1 year in class 10th. Different sets of number of students are there in class 9th for any two year. In class 10th, section P has 4 students and, Q, R, S have 2 students each.The below table gives the number of students in each section of class 9th over the years:Q. The top scorer was present in which section in 2013?

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A test was conducted in three sections X,Y,Z of tenth class. The average marks per student of sections X and Y together is 66. The average marks per student of sections Y and Z together is 63. The average marks per student of sections Z and X together is 67. The average marks per student of the three sections together is A. Find the number of integral values that A can take?
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A test was conducted in three sections X,Y,Z of tenth class. The average marks per student of sections X and Y together is 66. The average marks per student of sections Y and Z together is 63. The average marks per student of sections Z and X together is 67. The average marks per student of the three sections together is A. Find the number of integral values that A can take? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A test was conducted in three sections X,Y,Z of tenth class. The average marks per student of sections X and Y together is 66. The average marks per student of sections Y and Z together is 63. The average marks per student of sections Z and X together is 67. The average marks per student of the three sections together is A. Find the number of integral values that A can take? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A test was conducted in three sections X,Y,Z of tenth class. The average marks per student of sections X and Y together is 66. The average marks per student of sections Y and Z together is 63. The average marks per student of sections Z and X together is 67. The average marks per student of the three sections together is A. Find the number of integral values that A can take?.
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