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I would be tempted to pick E. The key is that you don't know how many students are in each class. It would seem that they want you to pick C though. I think they're trying to trick you into thinking that you can just algebraically determine the avg of the height in class Y by saying (120 + y) /2 = 126 which you can't do without knowing the number of students in each class (it's not an average of the two averages). What's the OA?

I would be tempted to pick E. The key is that you don't know how many students are in each class. It would seem that they want you to pick C though. I think they're trying to trick you into thinking that you can just algebraically determine the avg of the height in class Y by saying (120 + y) /2 = 126 which you can't do without knowing the number of students in each class (it's not an average of the two averages). What's the OA?

I agree with answer E. They are setting up a trap. We do not know the weighted average!

Let ∑Hx = Sum of heights of all students in class x
Nx = number of students in class x
The average height of students in class x = ∑Hx / Nx

Let ∑Hy = Sum of heights of all students in class y
Ny = number of students in class y
The average height of students in class y = ∑Hy / Ny

As per question, we need to find: ∑Hx / Nx / ∑Hy / Ny = (∑Hx / Nx) * (Ny * ∑Hy)

(1) The average height of the students in class X is 120 centimeters.
∑Hx / Nx = 120
This is not sufficient to solve the problem as we have no information on class y.

(2) The average height of the students in class X and class Y combined is 126 centimeters.
∑Hx / Nx + ∑Hy / Ny = 126

This is also not sufficient as it is not providing any information on Class x or Class y students information.

Considering both 1 and 2:

∑Hx / Nx + ∑Hy / Ny = 126 divide both sides by ∑Hx / Nx

∑Hx / Nx + ∑Hy / Ny = 126 which would give you a sum of the two averages, rather than a combination. Unfortunately, the rest of your calculations seem to hinge on this definition so I'm afraid it disconnects at this piont. Also, I think the OP mentioned OA was E.