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# What is the area of triangular region ABC above?

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Manager
Joined: 02 Dec 2012
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What is the area of triangular region ABC above?  [#permalink]

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03 Dec 2012, 03:54
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85% (00:57) correct 15% (01:27) wrong based on 1611 sessions

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What is the area of triangular region ABC above?

(1) The product of BD and AC is 20.
(2) x = 45
Math Expert
Joined: 02 Sep 2009
Posts: 50610
Re: What is the area of triangular region ABC above?  [#permalink]

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03 Dec 2012, 03:56
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What is the area of triangular region ABC above?

The area of triangle ABC = $$\frac{BD*AC}{2}$$

(1) The product of BD and AC is 20. The area of triangle ABC = $$\frac{BD*AC}{2}=\frac{20}{2}=10$$. Sufficient.
(2) x = 45. No lengths of any line segment is known. Not sufficient.

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Re: What is the area of triangular region ABC above?  [#permalink]

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03 Dec 2012, 07:19
What is the area of triangular region ABC above?

(1) The product of BD and AC is 20.
(2) x = 45

Case A:
BD is right-angled to AC (Given) in diagram, BD is height and AC is base of the triangle. Area can be calculated by 1/2* base X height. So, Sufficient.
Option C,E are eliminated.

Case B:
x = 45. Angle is not sufficient to find the area. This case is in-sufficient.
B is eliminated.

Intern
Joined: 07 May 2011
Posts: 31
Re: What is the area of triangular region ABC above?  [#permalink]

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04 Dec 2012, 19:39
1) area of triangle is half of the (base times altitude). which is 10. sufficient.
2) we are only given info on the the left portion divided by the altitude. the other portion area could be equal to the left portion or could be really elongated or small. can't tell. so not sufficient.

Attachment:
Area.png
What is the area of triangular region ABC above?

(1) The product of BD and AC is 20.
(2) x = 45
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Location: United States
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OG 13 Q73 Data Sufficiency  [#permalink]

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23 Mar 2015, 23:34
How can we know for sure that AD = DC or that AB=AC? This information is required for (1) to be sufficient and A to the correct answer.

If we look at the diagram they look equal but their is no proof in the information...

DO we assume in the GMAT that if the lines look equal they are equal? I always though this was a 'no no'
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OG 13 Q73 Data Sufficiency  [#permalink]

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24 Mar 2015, 00:21
2
mpcostello wrote:
How can we know for sure that AD = DC or that AB=AC? This information is required for (1) to be sufficient and A to the correct answer.

If we look at the diagram they look equal but their is no proof in the information...

DO we assume in the GMAT that if the lines look equal they are equal? I always though this was a 'no no'

Area of a triangle = 1/2 * base * height, and here the base is AC, while the height is BD.

Statement 1 tells us the product of the base and height, i.e. BD*AC = 20.
Since the question is asking about the area, we know that the area is 1/2 the product of BD and AC.
With this statement, we do NOT know for sure that AD = DC / AB = AC / the lines are equal... frankly we don't need to know for this statement to be sufficient. We have the product of BD and AC, and given that the area is half of the product, we have enough information to answer the question.

Statement 2 (that angle BAC, x, is 45 degrees) implies that ABC is isoceles (AB=BC), but this is NOT enough to give us any idea (on its own) about AC or BD. Hence this statement is insufficient and A is the answer.

Hope this helps.
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Re: What is the area of triangular region ABC above?  [#permalink]

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24 Mar 2015, 17:46
Area of a triangle = 1/2 * Base * Height ( product of BD and AC is known so the area is 10)
X=45 doesn't help to find out anything about the area.

Cheers !
Dhiraj

Attachment:
Area.png
What is the area of triangular region ABC above?

(1) The product of BD and AC is 20.
(2) x = 45

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Dhiraj Jha
http://www.globalmba-gyan.com
MBA 2011 - SDA Bocconi School of Management (Milan, Italy)
Global Account Management, Samsung Electronics Headquarters (Korea)

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Joined: 28 Jul 2015
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Re: What is the area of triangular region ABC above?  [#permalink]

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14 Oct 2015, 01:34
Bunuel, I understand that the statement 2 is insufficient. However, if there is a given number for AB side. Would the statement2 be sufficient to answer the question. Thanks in advance
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Re: What is the area of triangular region ABC above?  [#permalink]

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18 Oct 2015, 12:45
1
belley wrote:
Bunuel, I understand that the statement 2 is insufficient. However, if there is a given number for AB side. Would the statement2 be sufficient to answer the question. Thanks in advance

No. Even in this case we wouldn't know much about triangle BDC. Notice that we don;t know whether AB = BC.
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Re: What is the area of triangular region ABC above?  [#permalink]

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11 Dec 2017, 14:10
Hi All,

We're asked to figure out the area of triangular region ABC above. For that, we'll need the Area formula:

Area = (1/2)(Base)(Height)

So to answer this question, we either need the base and height of triangle ABC or we need the areas of the two smaller triangles.

(1) The product of BD and AC is 20.

Fact 1 tells us that the product of the height (BD) and the base (AC) = 20, so all we have to do is multiply that by 1/2 to get the area.... (1/2)(20) = 10
Fact 1 is SUFFICIENT

2) X = 45

This Fact tells us NOTHING about any of the side lengths, so there's no way to determine the area.
Fact 2 is INSUFFICIENT

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Re: What is the area of triangular region ABC above? &nbs [#permalink] 11 Dec 2017, 14:10
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