GMATPrepNow
What is the area of the shaded region in the figure shown?
(1) The area of the rectangle ABCD is 54.
(2) AE = 2ED
This is a (C) trap question designed in a way such that a test-taker may be tempted to believe that both statements are necessary for answering the question when, actually, only one is necessary.
Statement (1)This statement tells us two things: that the figure is a rectangle and that the area of the rectangle is 54.
We know that the area of a rectangle = b x h. So, b x h = 54.
Now, we have to find the area of the shaded region, and here's how the GMAT tempts us to choose the wrong answer: it breaks the shaded region into two triangles to make us start to wonder whether there are multiple possible areas of the shaded region, with the sizes of the different areas depending on how we draw those two triangles.
So, to correctly answer a question like this one, we have to be sure to see that the shapes of the two shaded triangles don't matter.
Why don't they matter? For one thing, regardless of the shape of the two shaded triangles, the large, unshaded triangle has the same base and height as the rectangle. Since the area of a triangle is always (b x h)/2, the area of the large triangle will always be half the area of the rectangle, regardless of the shapes of the two smaller triangles.
So, regardless of the shapes of the two smaller triangles, the area of the shaded region also will always be half of the area of the rectangle.
So, Statement (1) is sufficient.
Statement (2)Of course, we can easily tell that Statement (2) is insufficient, as it lacks any information on the area of anything in the figure, but a tricky aspect of Statement (2) is that it is designed to support the narrative that we need to have information on the shapes of the two smaller triangles in order to determine the area of the shaded region, as it provides some information on those shapes.
So, Statement (2) is designed to line up with the faulty thinking that the size of the area of the shaded region depends on the shapes of the two shaded triangles and tempt us to think that we need both statements and choose choice (C), as many people who have answered this question have.
So, the correct answer to this question is (A), and arriving at that answer requires avoiding being fooled by the way the question is constructed and seeing that, no matter where point E is on the base of the rectangle, the area of the shaded region is the same.