Author 
Message 
Senior Manager
Joined: 18 Aug 2009
Posts: 424
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0

5
This post was BOOKMARKED
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. \(AD \lt DC\) 2. \(AB \lt BC\) Source: GMAT Club Tests  hardest GMAT questions Could not understand GMAT club explanation, please elaborate.
_________________
Never give up,,,



CIO
Joined: 02 Oct 2007
Posts: 1218

Re: M18 Q4 [#permalink]
Show Tags
15 Jan 2010, 03:19
5
This post received KUDOS
2
This post was BOOKMARKED
It becomes easier if you draw a sketch for problems like this one. I'm attaching a sketch that I draw. So, we have two triangles ABD and CBD. BE is the height of both these smaller triangles as well as of the bigger triangle ABC. We know that a formula for finding the area of a triangle is \(\frac{1}{2}*base*height\). In our case the height is the same for both triangles (BE on the image below). So we need to know which of the bases is longer in order to tell which triangle has the greater area. S1 explicitly states that AD<DC. This is sufficient to know that the area of triangle ABD is smaller than that of triangle CBD. Since the height is the same, the longer base gives us the greater area. S2 is not sufficient because the lengths of AB and BC don't influence the area in this case. Imagine point D sliding to the right closer to the point C  this will increase the area of triangle ABD and decrease the area of triangle CBD. Notice that if we shift point D this way, the lengths of AB and BC don't change. Therefore, we don't really care about these values (AB and BC). I hope it helped .
Attachments
m1804.PNG [ 4.77 KiB  Viewed 7674 times ]
_________________
Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 21 Jul 2009
Posts: 364
Schools: LBS, INSEAD, IMD, ISB  Anything with just 1 yr program.

Re: M18 Q4 [#permalink]
Show Tags
15 Jan 2010, 07:30
dzyubam wrote: It becomes easier if you draw a sketch for problems like this one.
consider, BC is base and angle ABC is obtuse. Because, we can't be sure exactly how the figure looks like, we should take all possibilities in to consideration and I am guessing, both statements can help assert the required condition.\ My answer to the question is D.
_________________
I am AWESOME and it's gonna be LEGENDARY!!!



Senior Manager
Joined: 18 Aug 2009
Posts: 424
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0

Re: M18 Q4 [#permalink]
Show Tags
21 Jan 2010, 09:36
Great explanation, thank you
_________________
Never give up,,,



CIO
Joined: 02 Oct 2007
Posts: 1218

Re: M18 Q4 [#permalink]
Show Tags
22 Jan 2010, 01:17
1
This post received KUDOS
Angle ABC is obtuse in the image I attached above. S2 can't be sufficient, see explanation: Quote: S2 is not sufficient because the lengths of AB and BC don't influence the area in this case. Imagine point D sliding to the right closer to the point C  this will increase the area of triangle ABD and decrease the area of triangle CBD. Notice that if we shift point D this way, the lengths of AB and BC don't change. Therefore, we don't really care about these values (AB and BC). BC can't be the base as it's clearly stated in the question stem that point D lies on AC and we are dealing with triangles ABD and DBC. Can you draw a sketch to demonstrate how BC would be the base under the conditions given in the stem? I hope I'm not missing anything big here . BarneyStinson wrote: dzyubam wrote: It becomes easier if you draw a sketch for problems like this one.
consider, BC is base and angle ABC is obtuse. Because, we can't be sure exactly how the figure looks like, we should take all possibilities in to consideration and I am guessing, both statements can help assert the required condition.\ My answer to the question is D.
_________________
Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 20 Nov 2009
Posts: 6

Re: M18 Q4 [#permalink]
Show Tags
29 Jan 2010, 05:45
I sketched the diagram of the triangle and was able to arrive at a solution using the first statement, but the second statement alone is insufficient to arrive at an answer no matter how you draw it. I'm guessing the answer is A.



Intern
Joined: 28 Jan 2010
Posts: 3

Re: M18 Q4 [#permalink]
Show Tags
29 Jan 2010, 13:16
1
This post received KUDOS
Stmt1: If the AD = DC then both the triangle are equal and as shown in the picture both share the ame altitude and area is determined by which base is larger among the two.  Sufficient.
Stmt2: if AB < BC : the deciding factor still will be the proximity of D to A. If it is farther away from A, triangle ABD is greater.. Since no information about D is given  not Sufficient
Answer is A



Manager
Joined: 18 Oct 2009
Posts: 51
Location: Alberta, Canada
Schools: Queen's EMBA

Re: M18 Q4 [#permalink]
Show Tags
30 Jan 2010, 23:57
BarneyStinson wrote: dzyubam wrote: It becomes easier if you draw a sketch for problems like this one.
consider, BC is base and angle ABC is obtuse. Because, we can't be sure exactly how the figure looks like, we should take all possibilities in to consideration and I am guessing, both statements can help assert the required condition.\ My answer to the question is D. You have a good point but even with angle ABC obtuse, the area of triangles ABD and BDC cannot be compared if we do not get any info on D's location. S1 clarifies the location and compares the length of the bases of these triangles, so only answer is A!



Intern
Joined: 16 Jan 2011
Posts: 6
Schools: Arizona State University

Re: M18 Q4 [#permalink]
Show Tags
07 Feb 2011, 23:21
We need to figure out if Triangle ABD > Triangle DBC??
Based on s1 we know that base of Triangle DBC (i.e. DC) > base of Triangle ABD (i.e. AD). Now Area of triangle DBC is 1/2*BD*DC(1) and Area of triangle ABD is 1/2*BD*AD(2) As in both equations DC and AD are the only variables and based on s1 DC > AD therefore triangle ABD is NOT GREATER than triangle DBC. Hence S1 is SUFFICIENT.
Based on s2 AB < BC. This makes no difference in the formula of the area of both the triangles (i.e. triangle ABD and triangle DBC). Therefore S2 is NOT SUFFICIENT



Manager
Affiliations: The Earth organization, India
Joined: 25 Dec 2010
Posts: 191
WE 1: SAP consultantIT 2 years
WE 2: Entrepreneurfamily business 2 years

Re: M18 Q4 [#permalink]
Show Tags
06 Jul 2011, 00:33
I solved by median approach if d was mid point of side ac then the position of D decides whether smaller triangles are equal in area or unequal. There is an official guide 12 DS109 is based on similar lines. I had a small question if anyone can answer regarding the OA here  for any triangle abc, which has d as the point on BC, will the height of all 3 triangles be equal ?? {2 smaller and 1 larger triangle}
_________________
Cheers !!
Quant 47Striving for 50 Verbal 34Striving for 40



Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 176
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)

Re: M18 Q4 [#permalink]
Show Tags
07 Feb 2012, 07:33
My answer is D Statement 1: DC>AD since area of a triangle is 1/2*base*ht. Since both the traingles have the same height. So the triangle which has the larger base will have the largest area. Statement 2: A continuation of what is stated in the stimulus. Does provide any info for the area of triangle.



Math Expert
Joined: 02 Sep 2009
Posts: 39614

Re: M18 Q4 [#permalink]
Show Tags
07 Feb 2013, 06:47
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
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) \(AB<BC\) Consider the diagram below: Attachment:
m1804.PNG [ 4.77 KiB  Viewed 5011 times ]
Notice that \(BE\) is the height of the 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) \(AD<DC\). Sufficient. (2) \(AB<BC\). Not sufficient. Answer: A.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 15 Sep 2011
Posts: 361
Location: United States
WE: Corporate Finance (Manufacturing)

Re: M18 Q4 [#permalink]
Show Tags
26 May 2013, 11:47
1
This post received KUDOS
Bunuel wrote: 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) \(AB<BC\) Consider the diagram below: Attachment: m1804.PNG Notice that \(BE\) is the height of the 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) \(AD<DC\). Sufficient. (2) \(AB<BC\). Not sufficient. Answer: A. Thanks Bunuel, everyone, very helpful. One question, however, can you discuss the logic in creating line BE? Unfortunately, I don't "see the light", not fullyunderstanding, why we need to add an extra line there? Is it because we can't assume that BD is the height (and stemming from not completely grasping the principles of a triangle)? Thanks in advance for your insight



Math Expert
Joined: 02 Sep 2009
Posts: 39614

Re: M18 Q4 [#permalink]
Show Tags
27 May 2013, 00:56
mejia401 wrote: Bunuel wrote: 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) \(AB<BC\) Consider the diagram below: Attachment: m1804.PNG Notice that \(BE\) is the height of the 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) \(AD<DC\). Sufficient. (2) \(AB<BC\). Not sufficient. Answer: A. Thanks Bunuel, everyone, very helpful. One question, however, can you discuss the logic in creating line BE? Unfortunately, I don't "see the light", not fullyunderstanding, why we need to add an extra line there? Is it because we can't assume that BD is the height (and stemming from not completely grasping the principles of a triangle)? Thanks in advance for your insight Yes, we cannot assume that BD is the height. We are asked to compare the areas of the two triangles and for that we need the height.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 20 Oct 2013
Posts: 76
Location: United States
Concentration: General Management, Real Estate

Re: M18 Q4 [#permalink]
Show Tags
20 Apr 2014, 08:50
Using the formula of triangle area (=base*height/2) > only 1) is sufficient
Anyone understands why we need "ABC is the largest"?











