Isn't this a lot of calculation for a GRE question?

Answer: B
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WHAT WE HAVE:

118 juniors
Average(mean) score : 88

100 seniors
Average(mean) score : 92
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FIRST APPROACH (no need for calculations)
If the number of juniors was equal to seniors then mean would be mean of 92 and 88, so it would be 90, but now juniors are more than seniors and as their mean is less than 90, the total mean would be something less than 90. So B is bigger than A.
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SECOND APPROACH (with calculations)
A: The average (arithmetic mean) final exam score for all of the juniors and seniors combined
A = (total seniors score + total juniors score)/ (seniors population + juniors population)
A = (118*88 + 100*92) / (118+100) = (118*44 + 50*92) / ( 109) = 89.83
B = 90

So B is bigger than A.
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It doesn't need calculation actually and can be solve by approximation in 40 sec (including reading time)

-------APPROXIMATION STRATEGY + WEIGHTED AVG CONCEPT---------

118 juniors' average = 88
100 seniors' average = 92

Now if there were equal number of seniors & juniors, the combined average would come to be 90 (in the middle of the 2 independent averages).
But as juniors are more than seniors, the combined average would shift to their side i.e < 90.

Hence option A

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