GMAT Data Sufficiency- In the Picture Quadrilateral ABCD is a Parallelogram and Quadrilateral DEFG is a Rectangle

Question: In the picture, quadrilateral ABCD is a parallelogram and quadrilateral DEFG is a rectangle. What is the area of parallelogram ABCD (figure not drawn to scale)?

1. The area of rectangle DEFG is 8√5.
2. Line AH, the altitude of parallelogram ABCD, is 5

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.        
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.        
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.        
4. EACH statement ALONE is sufficient.        
5. Statements (1) and (2) TOGETHER are not sufficient.

“In the picture, quadrilateral ABCD is a parallelogram and quadrilateral DEFG is a rectangle.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:
There is only one approach to solve this problem.

Let us check by considering DC as base and EQ as height,
Area DEC = 1/2 * EQ * DC (1).

It also equals 1/2 Area ABCD (area of parallelogram is base * height). This is just normal formula.

The tricky part is how to link it with the rectangle DEFG.

Now, from C, we will draw a line CP that is perpendicular with DE with P is on DE.
Now, for triangle DEC, let us consider ED as base and CP as height.
We will heve an Area of DEC = 1/2 CP * DE (2)

From (1) and (2), the 2 area is the same, we have EQ * DC = CP * DE (3).
However, in rectangle DEFG, CP = EF (since DEFG is rectangle, CP perpendicular with DE, so CP must = EF)

So (3) can be rewritten as EQ * DC = EF * DE.
LHS is area of ABCD.
RHS is area of DEFG.
So statement 1 is sufficient. .

Correct Answer: A

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