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The students of three classes P, Q and R take a test. The average mark per student of P and Q put together is 60. The average mark per student of Q and R put together is 64. The average mark per student of P and R put together is 72. If the average mark per student of all the classes put together is x, which of the following is a possible value of x?
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The students of three classes P, Q and R take a test. The average mark...
Let the number of students in classes A, B and C be P, Q and R respectively.
Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R.
Also given that,
(83P + 76Q) / (P + Q) = 79
=> 4P = 3Q.
(76Q + 85R)/(Q + R) = 81
=> 4R = 5Q, => Q = 4P/3 and R = 5P/3
Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R)
= 978/12 = 81.5
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The students of three classes P, Q and R take a test. The average mark...
Solution:

Let us assume that the number of students in classes P, Q and R are P, Q and R respectively.

Average mark per student of P and Q put together is 60.

(P + Q) * 60 = (sum of marks scored by students of P and Q)

Average mark per student of Q and R put together is 64.

(Q + R) * 64 = (sum of marks scored by students of Q and R)

Average mark per student of P and R put together is 72.

(P + R) * 72 = (sum of marks scored by students of P and R)

The average mark per student of all the classes put together is x.

Total marks scored by all students of all classes taken together = (P + Q + R) * x

Adding the above three equations, we get:

(P + Q + R) * x = (sum of marks scored by students of P and Q) + (sum of marks scored by students of Q and R) + (sum of marks scored by students of P and R)

= 60(P + Q) + 64(Q + R) + 72(P + R)

= 60P + 60Q + 64Q + 64R + 72P + 72R

= 132P + 124Q + 136R

Therefore, x = [60(P + Q) + 64(Q + R) + 72(P + R)] / (P + Q + R)

= [132P + 124Q + 136R] / (P + Q + R)

= (132P / (P + Q + R)) + (124Q / (P + Q + R)) + (136R / (P + Q + R))

Let us assume that P = Q = R = 1 (to get a minimum value for x)

Then, x = (132/3) + (124/3) + (136/3) = 130

Let us assume that P = 1, Q = 2 and R = 3 (to get a maximum value for x)

Then, x = (132/6) + (124/6) + (136/6) = 64

Therefore, the possible values of x lie between 64 and 130.

Answer: Any value between 64 and 130 is a possible value of x.
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Directions:Read the information carefully to answer the question that follows.Dr. Ravi Patel teaches financial markets course at Indian Management Institute, which is being taught in two parts - one part in first trimester and the other part in second trimester. Initially, the professor divides the students randomly in five classes in first trimester and based on the performance of students in first trimester, he further divides the students of each class into two parts as below average and above average performers. It is observed that in each class, the ratio of below average and above average performers is at least 13/10.Initially, the classes were named as classes P, Q, R, S and T and after further division, the classes were renamed as classes 1, 2, 3, 4 ,....,10 and the classes in trimester 2 are named randomly i.e. it is not necessary that two parts of class A are numbered one after the other.It is also given that 1/5 of total students in first trimester were in class R, 23% of total students were in class Q and 17% of total students were in class T. The ratio of students in classes P and S was 11 : 9. In the second trimester, there were 20 students in class 1. The number of students in classes 3, 10 and 9 were twice, thrice and four times the number of students in class 1. The number of students in classes 4 and 5 are in ratio 1 : 3. The number of students in class 2 were 5 more than the number of students in class 9. The number of students in class 8 was 40% more than the number of students in class 4. The number of students in classes 6 and 7 is 50 and 30 and the total number of students in classes 4, 5 and 8 is 125% more than the number of students in class 10. Each student in first trimester was classified as either below average or above average performer.Q.What was the minimum difference between number of students who performed below average and number of students who performed above average in any class?

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The students of three classes P, Q and R take a test. The average mark per student of P and Q put together is 60. The average mark per student of Q and R put together is 64. The average mark per student of P and R put together is 72. If the average mark per student of all the classes put together is x, which of the following is a possible value of x?
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The students of three classes P, Q and R take a test. The average mark per student of P and Q put together is 60. The average mark per student of Q and R put together is 64. The average mark per student of P and R put together is 72. If the average mark per student of all the classes put together is x, which of the following is a possible value of x? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The students of three classes P, Q and R take a test. The average mark per student of P and Q put together is 60. The average mark per student of Q and R put together is 64. The average mark per student of P and R put together is 72. If the average mark per student of all the classes put together is x, which of the following is a possible value of x? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The students of three classes P, Q and R take a test. The average mark per student of P and Q put together is 60. The average mark per student of Q and R put together is 64. The average mark per student of P and R put together is 72. If the average mark per student of all the classes put together is x, which of the following is a possible value of x?.
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