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Math Expert V
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In the diagram above, coordinates are given for three of the vertices  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 72% (01:42) correct 28% (02:16) wrong based on 252 sessions

HideShow timer Statistics 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.

Attachment: cgpq_img2.png [ 10.71 KiB | Viewed 5388 times ]

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Re: In the diagram above, coordinates are given for three of the vertices  [#permalink]

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Bunuel wrote:
Attachment:
cgpq_img2.png
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.

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
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the diagram above, coordinates are given for three of the vertices  [#permalink]

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1
1
Quote:
ans D..
both the statements are sufficient..
1) it gives us x coord as 4 so the area of triangle above x axis =1/2*8*4=16... similarly below x axis=1/2*8*4=16... total 32 sufficient
2)parallelogram gives the area of two triangle on either side of x axis equal, so 16*2=32... thus sufficient

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.

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Re: In the diagram above, coordinates are given for three of the vertices  [#permalink]

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EMPOWERgmatRichC wrote:
Quote:
ans D..
both the statements are sufficient..
1) it gives us x coord as 4 so the area of triangle above x axis =1/2*8*4=16... similarly below x axis=1/2*8*4=16... total 32 sufficient
2)parallelogram gives the area of two triangle on either side of x axis equal, so 16*2=32... thus sufficient

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

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
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Re: In the diagram above, coordinates are given for three of the vertices  [#permalink]

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Bunuel wrote:
Attachment:
cgpq_img2.png
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.

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

Math Expert V
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Re: In the diagram above, coordinates are given for three of the vertices  [#permalink]

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Bunuel wrote: 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.

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.

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the diagram above, coordinates are given for three of the vertices  [#permalink]

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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?

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Re: In the diagram above, coordinates are given for three of the vertices  [#permalink]

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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= [AC*OD]*(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
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GMAT 1: 630 Q49 V27 Re: In the diagram above, coordinates are given for three of the vertices  [#permalink]

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Bunuel wrote:
Attachment:
The attachment cgpq_img2.png is no longer available
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.

Diagonals divided ||gram into two equal halves.
A is insufficient.
Attachments 23.jpg [ 41 KiB | Viewed 4274 times ]

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Posts: 13172
Re: In the diagram above, coordinates are given for three of the vertices  [#permalink]

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_________________ Re: In the diagram above, coordinates are given for three of the vertices   [#permalink] 13 Jan 2018, 13:55
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