rgg25 wrote:

What is the area of the quadrilateral with vertices A, B, C, and D?

(1) The perimeter of ABCD is equal to 16.

(2) Quadrilateral ABCD is a rhombus.

Why is the answer E? Is it b/c the the area of a rhombus (2) is not = to the area quoted in (1)?

I thought in regards to a Data insufficiency both statements (1) and (2) are to be taken as true.

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http://gmatclub.com/forum/best-gmat-books-77703.htmlComing to your question:

Q: What is the area of the quadrilateral with vertices A, B, C, and D?

Stem: We know that A,B,C,D are four points such that we can make a quadrilateral out of it. Question asks whether we can find out the area of the quadrilateral ABCD from the given information in Statement 1 and Statement 2. Then we look at St1 and St2 individually and check whether those statements are sufficient to answer the question that's asked. If not; if we use both statements together and see whether we will we be able to find the area then.

(1) The perimeter of ABCD is equal to 16.

Yes. We do treat the statement as true.

However, is this statement sufficient to answer the question i.e. to find the area of ABCD. The answer is NO, it is Not Sufficient.

Here's how.

What if ABCD is a square with side 4.

Perimeter of the square ABCD=4*4=16

Area of the square ABCD=4*4=16

What if ABCD is a rectangle with length=7 and width=1

Perimeter of the rectangle ABCD=2(7+1)=16

Area of the rectangle ABCD=7*1=7

So; we can have areas of ABCD as 16 or 7 based on this statement. Thus, this statement by itself is NOT SUFFICIENT to answer the question.

(2) Quadrilateral ABCD is a rhombus.

Now, we know that ABCD is a rhombus. But, to find the area of the rhombus we need the length of its diagonals OR Base and height of the rhombus OR length of side and measure of angle between them. We don't have any of those information. Thus, we won't be able to find the area of ABCD by using this statement. NOT SUFFICIENT.

Combining both statements; Now we are considering both statement 1 and statement 2 as TRUE together;

We know that ABCD is a rhombus and its perimeter is 16.

Well, we can have multiple rhombuses with perimeter 16 but varying area. Remember, if we keep shrinking the angle between two sides of a rhombus, the perimeter will remain same but the area will decrease from 90 degrees to 0 degrees. Thus, even after using both statements together we won't be able to find the area of the rhombus.

Both statements together are insufficient.

Ans: "E"

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~fluke

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