In the figure above, ABCD is a parallelogram and E is the midpoint of

Since we're asked to find a certain fraction, we can assign some nice values to the diagram (values that satisfy the given information!)

E is the midpoint of side AD
This means AE = ED
So, let's let AE = ED = 1
We get:


ABCD is a parallelogram
Property: Opposite sides in a parallelogram have equal lengths
Since AD = 2, it must also be the case that CB = 2



To find the areas of triangle ABE and trapezoid BCDE, we need the height of both shapes.
So, let's say the height of both shapes is 1



Area of triangle = (base)(height)/2

So, the area of ABE = (1)(1)/2 = 0.5


Area of trapezoid = (base1 + base2)(height)/2

So, the area of trapezoid BCDE = (1 + 2)(1)/2 = 3/2 = 1.5

The area of triangular region ABE is what fraction of the area of the quadrilateral region BCDE?
(area of triangular region ABE)/(area of the quadrilateral region BCDE) = 0.5/1.5 = 1/3

Answer: B

ALTERNATE SOLUTION
If you're unsure how to solve the question (or you're quite far behind timing-wise), you can apply the following property:
The diagrams in GMAT Problem Solving questions are DRAWN TO SCALE unless stated otherwise.
So, we may be able to use this fact to solve the question (or at least eliminate some answer choices before guessing) by simply "eyeballing" the diagram.

If we mentally connect points E and D to the midpoint of side BC, we got something like this:

At this point, it certainly looks like region ABE is approximately 1/3 the area of the quadrilateral region BCDE.
Guess C.