What is the area of the quadrilateral with vertices A, B, C, : GMAT Data Sufficiency (DS)
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What is the area of the quadrilateral with vertices A, B, C,

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What is the area of the quadrilateral with vertices A, B, C, [#permalink]

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New post 02 Apr 2011, 11:10
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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.
[Reveal] Spoiler: OA

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Re: Data insuffiency Q - Principles of the Data insuffiency [#permalink]

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New post 02 Apr 2011, 11:16
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1) insufficient
The geometry of the quadrilateral is unknown. Hence area is unknown.
2) insufficient
1) + 2) insufficient. The area of rhombus is the 1/2*product of diagonals. The latter is unknown. Hence E

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Re: Data insuffiency Q - Principles of the Data insuffiency [#permalink]

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New post 02 Apr 2011, 11:47
nicely put...simple explanation
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Re: Data insuffiency Q - Principles of the Data insuffiency [#permalink]

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New post 02 Apr 2011, 12:24
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.


Hello rgg25!! Welcome to the GMAT Club.

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http://gmatclub.com/forum/best-gmat-books-77703.html

Coming 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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Re: Data insuffiency Q - Principles of the Data insuffiency [#permalink]

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New post 03 Apr 2011, 06:42
1. Not sufficient

lets consider a rectangle here.

x+y = 8

we can have different combinations for x and y that satisfy the above condition and each of these combinations would yield a different xy , which the area.

1,7 => area 7
2,6 => area 12

2. Not sufficient . as we dont know anything about it . no info on rhombus - sides/perimeter


1& 2 together

to calculate the area of the rhomubs we need diagnal lengths or altitude or interior angles. we dont have any of these here.

we do have perimeter here, from which we can find the side. but thats not enough to find the area without knowing the above parameters.

Answer E
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New post 03 Apr 2011, 10:01
Very good and complete explanation

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Re: What is the area of the quadrilateral with vertices A, B, C, [#permalink]

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Re: What is the area of the quadrilateral with vertices A, B, C, [#permalink]

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New post 19 Dec 2015, 22:26
Statement 1: It could be any quadrilateral; parallelogram or not.

Statement 2: It's a rhombus. But the area of the rhombus depends on the diagonals, whose length depend upon the angles in the rhombus. For example, The rhombus could be just a square or could be a kit shaped. IN both cases, the variation is diagonal lenth is not proportional. Hence Insufficient even after we take the information from statement 1.

E None are sufficient
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Re: What is the area of the quadrilateral with vertices A, B, C,   [#permalink] 19 Dec 2015, 22:26
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