In the diagram above, coordinates are given for three of the vertices

Question

https://gmatclub.com/forum/download/file.php?id=25778 In the diagram above, coordinates are given for three of the vertices of quadrilateral ABCD. Does quadrilateral ABCD have an area greater than 30? (1) Point B has an x-coordinate of 4 (2) Quadrilateral ABCD is a parallelogram Kudos for a correct solution . cgpq_img2.png

chetan2u · Answer

ans B..
both the statements are sufficient..
1) it gives us x coord as 4 so the area of triangle above x axis requires y coord for height..although below x axis=1/2*8*4=16... insufficient
2)parallelogram gives the area of two triangle on either side of x axis equal, so 16*2=32... thus sufficient

EMPOWERgmatRichC · Answer

Hi chetan2u,

Your idea to separate the quadrilateral into two triangles is a good one. However, you made a slight logic mistake when dealing with the first Fact. Fact 1 gives us just the X-co-ordinate of point B. We're told that the X-coordinate is 4, which means that Point B is (4, Y). The Y co-ordinate of the pair is what is needed so that we can calculate the "height" of triangle ABC and we actually have almost NO information about that part of the co-ordinate. If we were told that the quadrilateral was a rectangle, parallelogram, etc. then we would be able to deduce the value of the Y, but without that information, we can only conclude that it's a positive number (and that's because the co-ordinate falls in the 1st Quadrant of the graph). The point could be (4, 1) or (4, 100) - these two possibilities would lead to two different answers to the given question. Thus, Fact 1 is INSUFFICIENT.

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

chetan2u · Answer

hi rich,
thanks .. you are absolutely correct... i dont know why i took x as the height... a mistake.. kudos for it ... editing the answer in light of this error

peachfuzz · Answer

The bottom triangle has an area of 16. If the area of the upper triangle is larger or smaller than 14, then we can determine if the area is greater than 30.

Statement 1:
We do not know the y coordinate, it could be any positive number.
Insufficient

Statement 2:
Since it is a parallelogram, the areas of the two triangles must be equal.
Sufficient

Answer: B

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

In this problem, the lower triangle ACD has a base of AC = 8, and a height, from the origin down to D, of 4. Therefore, the area of ACD = (1/2)(b)(h) = (1/2)(8)(4) = 16. We would need to know something about the upper triangle ABC to know the answer to the prompt question. We know the base of triangle ABC, AC = 8, but we don’t know anything about the height.

Statement #1: if we know the x-coordinate of point B, that doesn’t help us. We still know the base AC = 8, but we don’t know the height, only the vertical line along which point B will lie. Any height could be possible. This statement, alone and by itself, is insufficient.

Statement #2: the diagonal of any parallelogram (i.e. the line connecting two opposite vertices) divides it into two congruent triangles. Well, if ABCD is a parallelogram, then line AC is a diagonal, which means triangles ADC and ABD must be congruent and have equal area. This would allow us to calculate the total area and answer the prompt question. This statement, alone and by itself, is sufficient.

Answer = B

EMPOWERgmatRichC · Answer

Hi dkumar2012,

I'm going to give you some hints about how you can go about solving this question, so that you can re-attempt it:

Since the question asks about the relative area of the quadrilateral, you have to figure out a way to calculate if it's greater than 30 (or not).

Notice how the quadrilateral can be broken into 2 triangles (using the X-axis to split it in two). You CAN calculate the area of the "lower" triangle (remember Area = (1/2)(B)(H)). So you really just need to figure out the area of the "upper" triangle. What do you need to know to figure out THAT area....? And do the two Facts provide you with the proper information that you need?

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

D3N0 · Answer

In the diagram, coordinates are given for three of the vertices of quadrilateral ABCD. Does quadrilateral ABCD have an area greater than 30?

Ans: with already given information we know that triangle ABC and ADC are two triangle.
we know the area of triangle ADC is=  *(1/2)= 16
to get the are of Triangle ABC we need to know height of the triangle

(1): point B has an x-coordinate of 4
 It does not say anything about the height of triangle ABC. (Insufficient)

(2): quadrilateral ABCD is a parallelogram
 as it is parallelogram triangle ABC and ADC are the same triangle. (Properties: diagonal divides equally)
now we know the area of ABCD. we can answer the question. (Sufficient)

Ans:B

Lucky2783 · Answer

Answer B . 
Diagonals divided ||gram into two equal halves. 
A is insufficient.

mperalta · Answer

Why am I not getting the same result through the area = axb rule for regular quadrilaterals? Through pyth. side CD would be sqrt(52), and AD sqrt(20), which multiplied are 4 x sqrt(65), it would have to be 4 x sqrt(64) for it to give the same answer (32).

rahulp11 · Answer

Hi,

I was wondering if this system of thought/analysis would hold good for the same problem had Statement 2 were to be changed to say: "quadrilateral ABCD is a rectangle"?

Thanks

bumpbot · Answer

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In the diagram above, coordinates are given for three of the vertices

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In the diagram above, coordinates are given for three of the vertices

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