Author 
Message 
Manager
Joined: 13 Aug 2008
Posts: 54

2
This post received KUDOS
Is area of triangle \(ABC\) greater than area of triangle \(DEF\) ? 1. The value of area of \(ABC\) is less than that of perimeter of \(DEF\). 2. Angles of \(ABC\) = Angles of \(DEF\). Source: GMAT Club Tests  hardest GMAT questions



Intern
Joined: 03 May 2008
Posts: 33

Re: m07 #22 [#permalink]
Show Tags
03 Sep 2008, 21:23
Is the answer C?
Have you considered that both statements will give you the answer 'No'?
I tried using two 3,4,5 triangles: Area=6, and P=12 so satisfies constraint in Stmt 1
Stmt 2: tells us that triangles are similar.
Together, the answer is NO as in Area of traingle ABC is not Greater then EFG.
Alternatively, i tried using two 6,8,10 triangles, which gave me Area=24 and P=24 so didnt satisfy stmt 1.
Also, the triangle in your method should've been "1, 1, root2" or "10, 10, 10root2" (the isoscelese right triangle) Think of a square cut in half diagonally. If a square has side 10, then 10x10=100 > in half is 50.
Hope this helps and i hope i'm right!



Manager
Joined: 13 Aug 2008
Posts: 54

Re: m07 #22 [#permalink]
Show Tags
04 Sep 2008, 04:38
Ok, so the 101020 thing was a typo. I got confused with that...
If you know both the triangles are similar, the area could be less than or greater than the perimeter. I see my mistake, thanks ryan. But this only gives you info on the Area of ABC relative to the perimeter of ABC...statement (1) relates area ABC to perimeter DEF which we know nothing about.
345 P=12 Area=6 6810 P=24 Area=24 91215 P=36 Area=54
I think it is E after all.



Intern
Joined: 03 May 2008
Posts: 33

Re: m07 #22 [#permalink]
Show Tags
04 Sep 2008, 06:37
1
This post received KUDOS
Let me clarify....
I considered the case that ABC and DEF are BOTH 345 triangles.
Look at that list you made a little more closely.
345 P=12 Area=6 ............area is smaller than P 6810 P=24 Area=24 .......... area and P are equal 91215 P=36 Area=54 ..........area is greater than P
Using two 345 triangles satisfies the constraint in Stmt1, and then when stmt 2 confirms that the triangles are similar, stmt 1&2 gives us the definitive answer 'NO' to the question if Area of ABC is greater then EFG  because the area is equal.
Another consideration.... let's take a 6810 as ABC and 91215 as DEF: Stmt 1 is satisfied  Area ABC is less then P of DEF Stmt 2 is satisfied  They are similar triangles 1&2  together: Is area of ABC > DEF? .... NO it is not.
Make sense?



Manager
Joined: 10 Apr 2008
Posts: 53

Re: m07 #22 [#permalink]
Show Tags
23 May 2009, 20:59
I'm having some trouble understanding this question. I see why it doesn't work by picking numbers, but I always have a hard time doing that on the test. I feel like I might miss one set of numbers which is why I try to solve algebraically.
So can someone conceptually explain this?
If the two triangles are similar, then their areas would be proportionate too. (right?)



Intern
Joined: 09 Nov 2010
Posts: 9

Re: m07 #22 [#permalink]
Show Tags
18 Nov 2010, 11:40
Would someone please take a moment and explain to me why this is E and not C? Once you know that the angles are the same AND that the perimeter is bigger don't you have enough information to say that ABC is in fact not bigger?



Intern
Joined: 07 Nov 2010
Posts: 7
Schools: LSE, Erasmus University Rotterdam, Cass

Re: m07 #22 [#permalink]
Show Tags
18 Nov 2010, 13:23
mrcrescentfresh wrote: Would someone please take a moment and explain to me why this is E and not C? Once you know that the angles are the same AND that the perimeter is bigger don't you have enough information to say that ABC is in fact not bigger? The fact is that your reasoning works just for some types of triangles, while for others it doesn't. So, it must be E since both of them are too general. When I see question like these, it's a good idea not to waste too much time in experiments...the best idea is choosing E. Paolo



Manager
Status: Trying to get into the illustrious 700 club!
Joined: 18 Oct 2010
Posts: 78

Re: m07 #22 [#permalink]
Show Tags
18 Nov 2010, 14:49
1
This post received KUDOS
michael127 wrote: Is area of triangle \(ABC\) greater than area of triangle \(DEF\) ? 1. The value of area of \(ABC\) is less than that of perimeter of \(DEF\). 2. Angles of \(ABC\) = Angles of \(DEF\). Source: GMAT Club Tests  hardest GMAT questions I narrowed it down to C & E and chose the wrong answer. After looking at this problem for some time (waaaay more than 2 min I have an explanation)
1) Let's first try a 3:4:5 triangle. The area of a 3:4:5 triangle is 6 and the perimeter is 12. Now we go up to the question stem and we get NO.
Now that we have proven ABC is smaller than DEF we have to look for an instance where ABC is larger than DEF that would make statement 1) insufficient. If we make ABC a 2:2:2\sqrt{2} isosceles right triangle and DEF a 1:1:\sqrt{2} the area of ABC is 2 and the perimeter of DEF is 2 + \sqrt{2} (this makes the statement true).
We need to go to the question stem and plug this information in. The answer will be YES making statement 1 insufficient.
2) Statement 2 doesn't give us any information we can use.
Now the selections are C & E. Together the statements are not sufficient. So the answer is E.



Intern
Joined: 07 Sep 2010
Posts: 18

Re: m07 #22 [#permalink]
Show Tags
18 Nov 2010, 19:52
1
This post received KUDOS
S1: Area of ABC = 0.5 (b) (h) Perimeter of DEF = s1+s2+s3
0.5bh< s1+s2+s3 S2: not sufficient
Combining also there is no solution, so answer is E



Manager
Joined: 07 Jan 2010
Posts: 143
Location: So. CA
WE 1: 2 IT
WE 2: 4 Software Analyst

Re: m07 #22 [#permalink]
Show Tags
19 Nov 2010, 09:46
can someone give an example of where "The value of area of ABC is less than that of perimeter of DEF" and vice versa? Stmt1 is throwing me off!



Intern
Joined: 07 Sep 2011
Posts: 6

Re: m07 #22 [#permalink]
Show Tags
22 Nov 2011, 06:57
Assume: AB = BC = 2, Angle ABC = 90; DE = EF = 1, Angle DEF = ABC = 90. Area ABC = .5 * 2 * 2 = 2 Perimeter EDF = 1 + 1 + sqrt(2) > 2, but obviously Area ABD > Area DEF = 0.5.
The area of any triangle is the largest when it is a right triangle with both legs equal!



Manager
Joined: 01 Jan 2011
Posts: 67
Schools: INSEAD,IIMA,IIMB

Re: m07 #22 [#permalink]
Show Tags
23 Nov 2011, 00:46
simple geometry...the trick is in st 1: area of ABC is compared to perimeter of DEF..which does not lead us anywhere st2 itself does not help go for E
_________________
_________________________ Try and you will succeed !



Director
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 537
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)

Re: m07 #22 [#permalink]
Show Tags
22 Nov 2012, 06:25
michael127 wrote: Is area of triangle \(ABC\) greater than area of triangle \(DEF\) ? 1. The value of area of \(ABC\) is less than that of perimeter of \(DEF\). 2. Angles of \(ABC\) = Angles of \(DEF\). Source: GMAT Club Tests  hardest GMAT questions B. can NEVER answer the question, because other two angles can vary and so do the sides, so incorrect A. In given situation when the question is not limited to any specific angle consider the middle angle to be a right one, now even if it's a right angle 1/2 BC X AB = DE+EF+DF makes no sense ; incorrect E wins
_________________
" Make more efforts " Press Kudos if you liked my post



Senior Manager
Joined: 08 Jun 2010
Posts: 392
Location: United States
Concentration: General Management, Finance

Re: m07 #22 [#permalink]
Show Tags
22 Nov 2012, 19:55
Hi Bunuel, How do you eliminate A and C in this question?



Intern
Joined: 24 Sep 2012
Posts: 39

Re: m07 #22 [#permalink]
Show Tags
22 Nov 2012, 21:15
Hi All,
I have a doubt about the below. Can you please help?
If the triangles are similar, can we say... The ratio of their area is (side of one triangle)^2 / (side of other triangle)^2
Regards, Pritish



Math Expert
Joined: 02 Sep 2009
Posts: 39622

Re: m07 #22 [#permalink]
Show Tags
23 Nov 2012, 03:21



Intern
Joined: 20 Nov 2012
Posts: 4
Location: United States
Concentration: Technology, Organizational Behavior
GPA: 3.2
WE: Project Management (Computer Hardware)

Re: m07 #22 [#permalink]
Show Tags
23 Nov 2012, 07:24
I am such an idiot. I kept thinking same angles;same area...of course we can have different areas with the same angles.This is what a job does to your brains.#rusted



Manager
Joined: 12 Sep 2010
Posts: 232

Re: m07 #22 [#permalink]
Show Tags
17 Sep 2013, 14:01
I don't understand why Statement 1 is Insufficient even after I read the posts from above and the official explanation.
345 P=12 Area=6 ............area is smaller than P 6810 P=24 Area=24 .......... area and P are equal 91215 P=36 Area=54 ..........area is greater than P
The question asks: "Is area of triangle \(ABC\) greater than area of triangle \(DEF\) ?"
Statement 1's condition must be satisfy first before you can apply to the question. The perimeter must be GREATER than the area. After you satisfy St1 condition, then you can evaluate whether the area of triangle ABC is greater then area of triangle DEF. In ALL the cases in which the area is less than the perimeter, the area is also less than or equal to area of the triangle. There are no cases in which the area is less than the perimeter but have greater area.
St1: The value of area of \(ABC\) is less than that of perimeter of \(DEF\)
Here is the official explanation:
Statement (1) by itself is insufficient. Let's pick numbers: if the sides of \(ABC\) are 1, 1 and \(\sqrt{2}\) (a half of a square with sides equal to 1), the area equals \(0.5\) and t perimeter is \(2+\sqrt{2}\) . The perimeter is much greater than the area of a triangle with these values. However if the sides of \(ABC\) are 10, 10, and \(10\sqrt{2}\) ; then the perimeter is \(20+10\sqrt{2}\) and the area is 50. The perimeter is much smaller than the area.
The highlight portion of the OE contradicts the ST1 condition. Thus, its invalid. Can someone please explain the problem? Thanks.



HEC Thread Master
Joined: 06 May 2013
Posts: 97
Location: India
Concentration: Marketing, Technology
GMAT 1: 710 Q50 V35 GMAT 2: 730 Q49 V40
GPA: 2.8
WE: Consulting (Consulting)

Re: m07 #22 [#permalink]
Show Tags
18 Nov 2013, 06:37
Lets consider right angled triangles for the sake of simplicity:
I name them, a,b,c with area = 1/2*a*b and a',b',c' with area = 1/2*a'*b'.
Now, using statement 1, we have 1/2*a*b < a'+b'+c'. Using this, we need to see if we can arrive at some declarative result for 1/2*a*b>1/2*a'*b' (Yes or No). However, if you observe carefully, we can never be sure if the perimeter of a triangle is always less than or greater than its area. Hence option A and D are ruled out!
Now, using statement 2, we have all the angles to be equal, or the triangles to be similar. This has nothing to do with 1/2*a*b > 1/2*a'*b'. Hence, option B ruled out.
Using both the statements together we get, 1/2*a*b<a'+b'+c'. divide by 1/2*a'*b' on both sides. This will give us, a*b/a'*b' < (1/b' + 1/c' + c'/a'*b').
Now this value  (1/b' + 1/c' + c'/a'*b') can vary from less than 1 to more than 1, giving us more than one answers. Hence Option C is ruled out. Therefore, Option E is the right answer.



Current Student
Joined: 25 Sep 2012
Posts: 290
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34

Re: m07 #22 [#permalink]
Show Tags
12 May 2014, 09:33
is it really a good question? I'm still unable to judge what ability it is trying to test here? And is it possible to solve this sum under 2 mins or even 3 mins?











