Hi infiniti007,

This question is based on a rare Geometry rule. Notice the "white" triangle - one of it's sides 'shares' a side of the rectangle and the triangle 'touches' the opposite side of the rectangle. In this situation, the triangle is ALWAYS half the area of the rectangle. Since the white triangle is half the area, the two black triangles are the "other half" of the area.

To help you visualize this, draw a quick sketch of this picture. Next, draw a line "up" (re: perpendicular) from point E to the "top" of the rectangle. You now have 2 smaller rectangles and 4 triangles (2 sets of 2). Each min-rectangle is cut in "half" by the diagonal line that separates the triangles. Thus, half of each rectangle is white and half is black. That's further proof that the white triangle is half the area of the rectangle.

GMAT assassins aren't born, they're made,
Rich

Duplicate Post

Duplicate Post

infiniti007 wrote:

What is the area of the shaded region in the figure shown?

1.) The area of the rectangle ABCD is 54.
2.) AE = 2ED

As Mitch and Rich point out, the area of the shaded region will be HALF of the area of the entire rectangle. HOWEVER, if you didn't spot that, you can still solve the question as follows:

Target question: What is the area of the shaded region

Statement 1: The area of the rectangle ABCD is 54
Let's label the two shaded triangles as ∆1 and ∆2.
Also, let j be the length of the base of ∆1 and k be the length of the base of ∆2.
Let h = the height of both triangles (since ABCD is a RECTANGLE, the height is consistent for both ∆s)


Area of ∆ = (1/2)(base)(height)
So, (area of ∆1) + (area of ∆2) = [(1/2)(j)(h)] + [(1/2)(k)(h)]
= (1/2)(h)[j + k] [I factored out the (1/2)(h)]

IMPORTANT: j + k = the length of the BASE of rectangle ABCD.
In other words, (area of ∆1) + (area of ∆2) = (1/2)(h)[BASE of rectangle ABCD]
Since (h)(the BASE of rectangle ABCD) = the area rectangle ABCD, we can say that.....
(area of ∆1) + (area of ∆2) = HALF the area of rectangle ABCD

Since statement 1 tells us that the area of the rectangle ABCD is 54, we can conclude that (area of ∆1) + (area of ∆2) = (1/2)(54) = 27
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: AE = 2ED
IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

This technique can save a lot of time.

Here, we are told that line segment AE is TWICE the length of line segment ED.
Is this enough information to LOCK IN the combined areas of the two shaded triangles? NO.
Notice that statement 2 does not prohibit us from making rectangle ABCD are TALL or as SHORT as we want.


By making rectangle ABCD are TALL or as SHORT as we want, we can make the shaded area as large or as small as we wish.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A
--------------------------------------
ASIDE: Here are a few more DS Geometry questions to practice with:
- https://www.beatthegmat.com/good-ds-ques ... 70971.html
- https://www.beatthegmat.com/what-is-the- ... 74620.html
- https://www.beatthegmat.com/what-is-the- ... 77326.html
- https://www.beatthegmat.com/geometry-tri ... 71836.html
- https://www.beatthegmat.com/ds-2-t278892.html
- https://www.beatthegmat.com/coordinate-g ... 77659.html
--------------------------------------

Cheers,
Brent