TheCATExam
Sign in

CAT 2001 — QA Question 21

Weighted AverageEasy

Three math classes; X, Y, and Z, take an algebra test.

The average score in class X is 83.

The average score in class Y is 76.

The average score in class Z is 85.

The average score of all students in classes X and Y together is 79.

The average score of all students in classes Y and Z together is 81.

What is the average for all three classes?

Answer & solution

  • A

    81

  • 81.5

  • C

    82

  • D

    84.5

Solution

Let there be x number of students in class X, y number of students in class Y and z number of students in class Z.

∴ 83x + 76y = 79(x + y)

∴ 4x = 3y

Similarly,

76y + 85z = 81(y + z)

∴ 4z = 5y

∴ 20x = 15y = 12z

∴ x : y : z = 3 : 4 : 5

∴ The average of all the three classes

=83×3+76×4+85×53+4+5=81.5

Hence, option (b).

CAT 2001 QA Q21: Three math classes; X, Y, and Z, take an algebra test. The average score in class X is 83. The average score i — Solution | TheCATExam