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M18-04

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Bunuel
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M18-04 [#permalink] New post   16 Sep 2014, 01:02
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61% (01:37) correct 39% (02:01) wrong based on 337 sessions
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If, in triangle \(ABC\), angle \(ABC\) is the largest and point \(D\) lies on segment \(AC\), is the area of triangle \(ABD\) larger than that of triangle \(DBC\)?


(1) \(AD < DC\)

(2) \(AB < BC\)
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Bunuel
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Re M18-04 [#permalink] New post   16 Sep 2014, 01:03
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Official Solution:


If, in triangle \(ABC\), angle \(ABC\) is the largest and point \(D\) lies on segment \(AC\), is the area of triangle \(ABD\) larger than that of triangle \(DBC\)?

Consider the diagram below:



Notice that \(BE\) is the height of triangle \(ABC\). Now, the area of triangle \(ABD\) is \(\frac{1}{2}*height*base = \frac{1}{2}*BE*AD\), and the area of triangle \(DBC\) is \(\frac{1}{2}*height*base=\frac{1}{2}*BE*DC\). So, we can see that the area of triangle \(ABD\) will be greater than the area of triangle \(DBC\) if \(AD\) is greater than \(DC\).

(1) \(AD \lt DC\). Sufficient.

(2) \(AB \lt BC\). Not sufficient.


Answer: A
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priyankasharma123
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Re: M18-04 [#permalink] New post   14 Jul 2015, 18:52
Hi,

Why can't i change my base as in either BD ,AB,BC.
In this case my height will vary.
Please explain how come you have height to be BE and not (BD,AB,BC).

Thanks
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chetan2u
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Re: M18-04 [#permalink] New post   14 Jul 2015, 20:28
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priyankasharma123 wrote:
Hi,

Why can't i change my base as in either BD ,AB,BC.
In this case my height will vary.
Please explain how come you have height to be BE and not (BD,AB,BC).

Thanks


hi,
irrespestive of what height depending on the base we take, the area will remain the same..
Since here we have a height and a base and the area of triangle depends on the base as the height in this case will be the same and thus only one variable involved, Why should we complicate the things by taking a bases , which are not the same resulting in different heights and thus two variables..
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Re: M18-04 [#permalink] New post   09 Jul 2016, 04:14
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I think this is a high-quality question and I agree with explanation.
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dharan
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Re: M18-04 [#permalink] New post   31 Jul 2016, 06:49
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I think this is a high-quality question and I agree with explanation. I have another approach.

Triangle Median property
1. The median of the triangle divides the triangle into two smaller triangles which have the same area.
In this case point D is not a median. Applying above property on statement 1 we can say area of triangle ABD > area of triangle DBC.

Statement 2 clearly not sufficient.
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Bunuel
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Re: M18-04 [#permalink] New post   23 Jun 2023, 01:34
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M18-04 [#permalink] New post   22 Dec 2023, 13:04
Dear Bunuel, how can A be the correct answer if S1 says AD<DC ? Could you please clarify ?
Thanks .

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Bunuel
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Re: M18-04 [#permalink] New post   22 Dec 2023, 13:16
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bsolly wrote:
Bunuel wrote:
Official Solution:


If, in triangle \(ABC\), angle \(ABC\) is the largest and point \(D\) lies on segment \(AC\), is the area of triangle \(ABD\) larger than that of triangle \(DBC\)?

Consider the diagram below:



Notice that \(BE\) is the height of triangle \(ABC\). Now, the area of triangle \(ABD\) is \(\frac{1}{2}*height*base = \frac{1}{2}*BE*AD\), and the area of triangle \(DBC\) is \(\frac{1}{2}*height*base=\frac{1}{2}*BE*DC\). So, we can see that the area of triangle \(ABD\) will be greater than the area of triangle \(DBC\) if \(AD\) is greater than \(DC\).

(1) \(AD \lt DC\). Sufficient.

(2) \(AB \lt BC\). Not sufficient.


Answer: A



Dear Bunuel, how can A be the correct answer if S1 says AD<DC ? Could you please clarify ?
Thanks .

Posted from my mobile device


The area of triangle \(ABD\) will be greater than the area of triangle \(DBC\) if \(AD\) is greater than \(DC\). (1) says that \(AD \lt DC\). Hence, the area of triangle \(ABD\) is NOT greater than the area of triangle \(DBC\). We have a definite NO answer to the question. Sufficient.

P.S. Recall that a definitive 'no' is as valid as a 'yes' in establishing sufficiency. The critical factor in GMAT Data Sufficiency is not whether the answer is positive or negative, but whether the data provided conclusively supports that answer. A consistent 'no' can effectively fulfill the question's requirement, confirming the sufficiency of the data.
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Re: M18-04 [#permalink] New post   31 Jan 2024, 20:00
Bunuel, what is the importance of angle ABC being the largest one? Would the answer change if that angle weren't the largest?
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Re: M18-04 [#permalink] New post   31 Jan 2024, 20:54
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andreagonzalez2k wrote:
Bunuel, what is the importance of angle ABC being the largest one? Would the answer change if that angle weren't the largest?



The answer will not change. ABC being the largest angle does not have any affect on the question.
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Re: M18-04 [#permalink]
31 Jan 2024, 20:54
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