M18-04

Question

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

Bunuel · Accepted Answer

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:
 
 https://gmatclub.com/gmat-practice-tests/resources/import/img/m18-04.png 
 
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

priyankasharma123 · Answer

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

chetan2u · Answer

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..

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation.

dharan · Answer

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.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

bsolly · Answer

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

Posted from my mobile device

Bunuel · Answer

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.

andreagonzalez2k · Answer

Bunuel, what is the importance of angle ABC being the largest one? Would the answer change if that angle weren't the largest?

chetan2u · Answer

The answer will not change. ABC being the largest angle does not have any affect on the question.

M18-04

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