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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   55% (hard)

Question Stats: 57% (01:20) correct 43% (01:29) wrong based on 220 sessions

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If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?

(1) $$|x| = y = 10$$

(2) $$x = |y| = 10$$

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Math Expert V
Joined: 02 Sep 2009
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Official Solution:

If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?

Statement 1: If $$|x| = y = 10$$, $$y$$ is 10 but $$x$$ could be -10 or 10. The area is same for $$x = 10$$ and $$x = -10$$. This is sufficient to answer the question.

Statement 2: If $$x = |y| = 10$$, $$x = 10$$ but $$y$$ could be 10 or -10 but different value of $$y$$ does not affect the area of the triangle. This statement is also sufficient to answer the question.

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1
Bunuel wrote:
Official Solution:

Statement 1: If $$|x| = y = 10$$, $$y$$ is 10 but $$x$$ could be -10 or 10. The area is same for $$x = 10$$ and $$x = -10$$. This is sufficient to answer the question.

Statement 2: If $$x = |y| = 10$$, $$x = 10$$ but $$y$$ could be 10 or -10 but different value of $$y$$ does not affect the area of the triangle. This statement is also sufficient to answer the question.

Can you please explain statement one in more detail i.e. how area is same .
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If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?

(1) |x| = y = 10

(2) x = |y| = 10

Given that vertices of a triangle are A (5, 0) and C (25, 0) =>Two vertices of the triangle are on x-axis =>Base = 20.
Area of a triangle = 1/2*(base)*(height)
Since, base is given, area of the triangle can be found if any of the following statement uniquely provide height of the triangle.

Statement 1:
|x| = y = 10
Or, x point lies on the line y=10 => height of the triangle=10 => sufficient.....(B)(C)(E)
Statement 2:
x = |y| = 10
Or, y point lies on the line x=10 => height of the triangle =10 => sufficient.....(A)(D)

Math Expert V
Joined: 02 Sep 2009
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simi200207 wrote:
Bunuel wrote:
Official Solution:

Statement 1: If $$|x| = y = 10$$, $$y$$ is 10 but $$x$$ could be -10 or 10. The area is same for $$x = 10$$ and $$x = -10$$. This is sufficient to answer the question.

Statement 2: If $$x = |y| = 10$$, $$x = 10$$ but $$y$$ could be 10 or -10 but different value of $$y$$ does not affect the area of the triangle. This statement is also sufficient to answer the question.

Can you please explain statement one in more detail i.e. how area is same .

Look at the diagram below:
Attachment:
Untitled.png
Notice that no matter where point B is (blue or green dot) the area of the triangle would be the same, because the base (red segment) and the height would be the same.
>> !!!

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The graph makes it clearer....thanks Bunuel.
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1
Bunuel wrote:
If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?

(1) $$|x| = y = 10$$

(2) $$x = |y| = 10$$

Dear Bunuel,

Please correct me, if my reasoning for the above question is wrong.

The two specified co-ordinates will be on X-Axis.
(1) Y = 10 and the co-ordinate of x can be either 10 or -10, but in both the cases, X will lie on a straight line that is parallel to X Axis, thus we can use the Triangle area concept that if two points of a triangle lie on a line then the all the triangles formed with the third point on the parallel line will have the same area.

(2) The same concept can be used here. Though in this case, it is visible that the two triangles formed will be mirror image of each other, thus even in this case the area can be known.

Thus Answer should be D
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Bunuel wrote:
Official Solution:

Statement 1: If $$|x| = y = 10$$, $$y$$ is 10 but $$x$$ could be -10 or 10. The area is same for $$x = 10$$ and $$x = -10$$. This is sufficient to answer the question.

Statement 2: If $$x = |y| = 10$$, $$x = 10$$ but $$y$$ could be 10 or -10 but different value of $$y$$ does not affect the area of the triangle. This statement is also sufficient to answer the question.

Hi Bunuel,

Is it the value of x that doesnt affect the area of the triangle not the value of y?
Math Expert V
Joined: 02 Sep 2009
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vietnammba wrote:
Bunuel wrote:
Official Solution:

Statement 1: If $$|x| = y = 10$$, $$y$$ is 10 but $$x$$ could be -10 or 10. The area is same for $$x = 10$$ and $$x = -10$$. This is sufficient to answer the question.

Statement 2: If $$x = |y| = 10$$, $$x = 10$$ but $$y$$ could be 10 or -10 but different value of $$y$$ does not affect the area of the triangle. This statement is also sufficient to answer the question.

Hi Bunuel,

Is it the value of x that doesnt affect the area of the triangle not the value of y?

For the first statement it's the value of x and for the second one it's the value of y.
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Bunuel wrote:
simi200207 wrote:
Bunuel wrote:
Official Solution:

Statement 1: If $$|x| = y = 10$$, $$y$$ is 10 but $$x$$ could be -10 or 10. The area is same for $$x = 10$$ and $$x = -10$$. This is sufficient to answer the question.

Statement 2: If $$x = |y| = 10$$, $$x = 10$$ but $$y$$ could be 10 or -10 but different value of $$y$$ does not affect the area of the triangle. This statement is also sufficient to answer the question.

Can you please explain statement one in more detail i.e. how area is same .

Look at the diagram below:
Attachment:
Untitled.png
Notice that no matter where point B is (blue or green dot) the area of the triangle would be the same, because the base (red segment) and the height would be the same.

Dear Bunuel, that is the same what i am draw and that is what i am ask for. In the green triangle I need to

understand which side is the height and how it equal to 10.I really confused   _________________

Click +1 Kudos if my post helped

Math Expert V
Joined: 02 Sep 2009
Posts: 53657

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3
23a2012 wrote:
Bunuel wrote:
Bunuel wrote:
Official Solution:

Statement 1: If $$|x| = y = 10$$, $$y$$ is 10 but $$x$$ could be -10 or 10. The area is same for $$x = 10$$ and $$x = -10$$. This is sufficient to answer the question.

Statement 2: If $$x = |y| = 10$$, $$x = 10$$ but $$y$$ could be 10 or -10 but different value of $$y$$ does not affect the area of the triangle. This statement is also sufficient to answer the question.

Look at the diagram below:
Attachment:
Untitled.png
Notice that no matter where point B is (blue or green dot) the area of the triangle would be the same, because the base (red segment) and the height would be the same.

Dear Bunuel, that is the same what i am draw and that is what i am ask for. In the green triangle I need to

understand which side is the height and how it equal to 10.I really confused   I think that you really need to brush up fundamentals on geometry.
>> !!!

You do not have the required permissions to view the files attached to this post.

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according to coordinate geometry graph the answer should be B
Math Expert V
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arjungmat wrote:
according to coordinate geometry graph the answer should be B

The answer is NOT B, it's D. Please check the discussion above and ask if anything is unclear.
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I think this the explanation isn't clear enough, please elaborate.
Intern  Joined: 07 Mar 2016
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Height of triangle is to be drawn perpendicular to base from third co ordinate. In this case base has to be extended towards left where perpendicular from third co ordinate meets the base. Hope this would make little bit clear
Manager  B
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I am wondering why the formula to calculate the area of an triangle with coordinations of 3 verticles cannot work.
Intern  B
Joined: 01 Jan 2017
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GMAT 1: 730 Q50 V38 ### Show Tags

I am also trying to understand, whether Hero's formula or Deterinant method to calculate triangle area can also help proove that the sign of x or y do not matter.
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Joined: 30 Oct 2016
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I don't agree with the explanation. USING STATEMENT 1 WE WILL GET 2 COORDINATES BUT AREA USING THE 2 COORDINATES WILL BE DIFFERENT.
BUT USING STATEMENT 2 THE AREA OF THE TRIANGLE USING BOTH THE COORDINATES WILL BE SAME.

SO THE ANSWER SHOULD BE B
Math Expert V
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samism wrote:
I don't agree with the explanation. USING STATEMENT 1 WE WILL GET 2 COORDINATES BUT AREA USING THE 2 COORDINATES WILL BE DIFFERENT.
BUT USING STATEMENT 2 THE AREA OF THE TRIANGLE USING BOTH THE COORDINATES WILL BE SAME.

SO THE ANSWER SHOULD BE B

First of all, please turn of caps lock when posting. Next, please read the whole discussion before posting. For example, check this post: https://gmatclub.com/forum/d01-183495.html#p1481313
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chessgiants wrote:
I am wondering why the formula to calculate the area of an triangle with coordinations of 3 verticles cannot work.

Hi,

I am guessing it will work here. Please correct me if I am wrong.

Area = |5(y-0) + x(0-0) + 25*(0-y)| / 2

Area = |5y - 25y| / 2

Both equations will give the value of y and you will get the same answer whether y is 10 or -10. Re: D01-34   [#permalink] 30 Sep 2017, 03:49

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