|
Author |
Message |
|
TAGS:
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12098
Followers: 1876
Kudos [?]:
10096
[4] , given: 959
|
Is the perimeter of triangle ABC greater than 20? (1) [#permalink]
 19 Nov 2009, 18:40
4
This post received
KUDOS
Question Stats:
34% (02:27) correct
65% (01:38) wrong based on 43 sessions
|
|
|
|
|
|
|
Senior Manager
Joined: 30 Aug 2009
Posts: 295
Location: India
Concentration: General Management
Followers: 2
Kudos [?]:
65
[0], given: 5
|
Re: Perimeter of triangle ABC. [#permalink]
19 Nov 2009, 19:25
Bunuel wrote: Is the perimeter of triangle ABC greater than 20?
(1) BC-AC=10.
(2) The area of the triangle is 20. will go with A 1. BC = 10+AC. If BC is the longest side then going by the rule that sum of the 2 smaller sides of triangle will be more than the larger side we will get perimeter more than 20. suff 2. we can get sides as 8,5,4 and 10,4,7 satisying that area is 20. for 8,5,4 perimeter is 17 and for 10,4,7 perimeter is 21. hence insuff
|
|
|
|
|
|
Manager
Joined: 13 Oct 2009
Posts: 115
Location: USA
Schools: IU KSB
Followers: 4
Kudos [?]:
42
[1] , given: 66
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 07:24
1
This post received
KUDOS
Bunuel wrote: Is the perimeter of triangle ABC greater than 20?
(1) BC-AC=10.
(2) The area of the triangle is 20. I pick 'A' (1) Sides AB, BC, AC Given BC-AC=10 BC=AC+10 BC>10
And BC-AC< AB <BC+AC so AB >10so whatever is the value of AC AB+BC+AC >20 Sufficient (2) Since type of triangle is not given, it is not possible to find only one set of lengths of sides. Not Sufficient
|
|
|
|
|
|
Senior Manager
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 319
Followers: 2
Kudos [?]:
78
[0], given: 37
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 07:34
Answer A basing S1 on the rule that " the length of a triangle is always greater than the absolute difference of the lengths of other two sides" we know that other side must be > 10 and from S1 we know that atleast one other side is 10, hence sufficient. S2) not sufficient. ab=40, a,b can be 5,8 or 2, 20
_________________
Thanks, Sri
-------------------------------
keep uppp...ing the tempo...
Press +1 Kudos, if you think my post gave u a tiny tip
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12098
Followers: 1876
Kudos [?]:
10096
[0], given: 959
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 09:27
|
|
|
|
|
|
Intern
Joined: 11 Nov 2009
Posts: 10
Followers: 0
Kudos [?]:
0
[0], given: 1
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 12:04
The answer should be C.
The explanation for why Statement 1 is sufficient is already given above
For Statement 2 it is stated that Area = 20
=> 1/2*B*H = 20 or B*H = 40.
If we look at the possible twin factors that could yield 40 we have {1,40}, {2,20}...{5,8}..
If we consider the base to be any one of the numbers occuring in the twin factors, and the height to be the other number, both the sides other than the base will always have a length that is greater than the height.
This implies that the perimeter will always be greater than 20 if the area is 20.
|
|
|
|
|
|
Intern
Joined: 18 Nov 2009
Posts: 48
Followers: 1
Kudos [?]:
7
[0], given: 2
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 12:26
I go for D each statement alone is suff.
(1) is evident
(2) is more tricky but going for one extrem (base, height) (40,1) to the other (1, 40) and the mid-couple (20, 2), the perimeter will seemingly always be greater than 20.
OA?
|
|
|
|
|
|
Manager
Joined: 29 Oct 2009
Posts: 212
Followers: 49
Kudos [?]:
419
[5] , given: 18
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 13:19
5
This post received
KUDOS
Question Stem : Is AB + BC + AC > 20?
St. (1) : BC = AC + 10
Triangle Property : The sum of any two sides of a triangle is always greater than the third.
Since we are given that one of the sides is greater than 10, the sum of the other two sides must also be greater than 10. Hence the perimeter will always be greater than 20. Statement is sufficient. St. (2) : A = 40
Triangle Property : For triangles with same area, the perimeter is smallest for an equilateral triangle.
Area of equilateral triangle with side x = \frac{\sqrt{3}}{4}x^2Therefore, \frac{\sqrt{3}}{4}x^2 = 40 x^2 = \frac{160}{\sqrt{3}}Now, in order to speed up calculations, I will assume \sqrt{3} to be equal to 2. If the condition is satisfied with \sqrt{3} equal to 2 then it will definitely be satisfied with the actual value of \sqrt{3} which is less than 2. Therefore, x^2 = \frac{160}{2} = 80 This tells us that x is almost 9. More importantly, it tells us that x is greater than 8. Thus perimeter will be 3*x = 24. Since this is the minimum perimeter possible (actually it is still less than what the actual minimum would be due to our approximations), we can conclude that the question stem will always be true. Hence Sufficient. Answer : D
Another interesting triangle property : For triangles with same perimeter, the area is maximum for an equilateral triangle. (If you think about it, this property goes hand in hand with the one we used in St. 2).
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders!
compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942
Word Problems Made Easy!
1) Translating the English to Math : word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : distance-speed-time-word-problems-made-easy-87481.html
|
|
|
|
|
|
CEO
Joined: 29 Aug 2007
Posts: 2528
Followers: 41
Kudos [?]:
364
[2] , given: 19
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 13:30
2
This post received
KUDOS
Bunuel wrote: Is the perimeter of triangle ABC greater than 20?
(1) BC-AC=10.
(2) The area of the triangle is 20. AB+AC+BC = 20? Use third-side rule: The third side cannot be > sum of the rest two sides and smaller than the difference of the two sides: traingle-sides-85784.html#p643924Also: The smallest perimeter is of the equilateral triangle for a given area or perimeter. 1: BC-AC=10. BC>10 AC>0 AB>BC-AC Add up these all: AB+AC+BC > 10+0+BC-AC AB+AC+BC > 10+0+(10+x) where x>0 AB+AC+BC > 20+x. Suff. 2: The area of the triangle is 20. The smallest perimeter of this triangle is s if the triangle is equilateral. If so, s is: 20 = s^2 (Sqrt3/4) s^2 = 80/(Sqrt 3) s = 6.8 Perimeter = 3s = 3(6.8) = 20.40>20. SUFF. D.
_________________
Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
GT
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12098
Followers: 1876
Kudos [?]:
10096
[0], given: 959
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 13:42
sriharimurthy wrote: Question Stem : Is AB + BC + AC > 20?
St. (1) : BC = AC + 10
Triangle Property : The sum of any two sides of a triangle is always greater than the third.
Since we are given that one of the sides is greater than 10, the sum of the other two sides must also be greater than 10.
Hence the perimeter will always be greater than 20.
Statement is sufficient.
St. (2) : A = 40
Triangle Property : For triangles with same area, the perimeter is smallest for an equilateral triangle.
Area of equilateral triangle with side x = \frac{\sqrt{3}}{4}x^2
Therefore, \frac{\sqrt{3}}{4}x^2 = 40
x^2 = \frac{160}{\sqrt{3}}
Now, in order to speed up calculations, I will assume \sqrt{3} to be equal to 2.
If the condition is satisfied with \sqrt{3} equal to 2 then it will definitely be satisfied with the actual value of \sqrt{3} which is less than 2.
Therefore, x^2 = \frac{160}{2} = 80
This tells us that x is almost 9. More importantly, it tells us that x is greater than 8. Thus perimeter will be 3*x = 24.
Since this is the minimum perimeter possible (actually it is still less than what the actual minimum would be due to our approximations), we can conclude that the question stem will always be true.
Hence Sufficient.
Answer : D
Another interesting triangle property : For triangles with same perimeter, the area is maximum for an equilateral triangle. (If you think about it, this property goes hand in hand with the one we used in St. 2).
Yes, the OA is D. It was the hard one. This problem could be solved knowing the properties sriharimurthy mentioned. +1. For (1): The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides. For (2): A. For a given perimeter equilateral triangle has the largest area.
B. For a given area equilateral triangle has the smallest perimeter.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 29 Oct 2009
Posts: 212
Followers: 49
Kudos [?]:
419
[0], given: 18
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 14:02
Thanks Bunuel. Though I just realized something. I considered the area given to be 40 by mistake. It is actually 20. Although the logic will be same, the calculations will be harder since we will have to use the real value of \sqrt{3}. (no margin for approximations!) Sorry for the mistake guys. However, as long as you understand the logic, it shouldn't matter. At least you'll know how to go about approaching such questions in the future! Cheers. Ps. Any trick for the calculations Bunuel?
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders!
compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942
Word Problems Made Easy!
1) Translating the English to Math : word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : distance-speed-time-word-problems-made-easy-87481.html
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12098
Followers: 1876
Kudos [?]:
10096
[2] , given: 959
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 14:29
2
This post received
KUDOS
sriharimurthy wrote: Thanks Bunuel.
Though I just realized something. I considered the area given to be 40 by mistake. It is actually 20.
Although the logic will be same, the calculations will be harder since we will have to use the real value of \sqrt{3}. (no margin for approximations!)
Sorry for the mistake guys. However, as long as you understand the logic, it shouldn't matter. At least you'll know how to go about approaching such questions in the future!
Cheers.
Ps. Any trick for the calculations Bunuel? I would go backward. Let's assume the perimeter is 20. The largest area with given perimeter will have the equilateral triangle, so side=20/3. Let's calculate the area and if the area will be less than 20 it'll mean that perimeter must be more than 20. Area=s^2*\frac{\sqrt{3}}{4}=(\frac{20}{3})^2*\frac{\sqrt{3}}{4}=\frac{100*\sqrt{3}}{9}=~\frac{173}{9}<20Think this way is easier. \sqrt{3}\approx{1.73}.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 29 Oct 2009
Posts: 212
Followers: 49
Kudos [?]:
419
[0], given: 18
|
Re: Perimeter of triangle ABC. [#permalink]
20 Nov 2009, 14:32
Quote: I would go backward.
Let's assume the perimeter is 20. The largest are with given perimeter would have the equilateral triangle, so side=20/3. Let's calculate the area and if the area will be less than 20 it'll mean that perimeter must be more than 20.
Think this way is easier.
Yes. You are right. It will be easier. Thanks!
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders!
compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942
Word Problems Made Easy!
1) Translating the English to Math : word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : distance-speed-time-word-problems-made-easy-87481.html
|
|
|
|
|
|
Intern
Joined: 10 Dec 2010
Posts: 2
Followers: 0
Kudos [?]:
0
[0], given: 19
|
Geometry
Is the perimeter of triangle ABC greater than 20?
(1) BC-AC=10.
(2) The area of the triangle is 20.
Please help to solve this best
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12098
Followers: 1876
Kudos [?]:
10096
[0], given: 959
|
|
|
|
|
|
|
Intern
Joined: 02 Sep 2010
Posts: 48
Location: India
Followers: 0
Kudos [?]:
15
[1] , given: 17
|
1
This post received
KUDOS
shubhranaidu wrote: Geometry
Is the perimeter of triangle ABC greater than 20?
(1) BC-AC=10.
(2) The area of the triangle is 20.
Please help to solve this best Stmt1 says: BC-AC=10, which implies BC>10, and by property of triangles AB>10. This means AB+BC > 20, So Perimeter>20 ie. stmt1 is suff. Stmt2 says: Area = 20, Area > Perimeter, implies perimter <20, i.e stmt2 is suff. OA is C.
_________________
The world ain't all sunshine and rainbows. It's a very mean and nasty place and I don't care how tough you are it will beat you to your knees and keep you there permanently if you let it. You, me, or nobody is gonna hit as hard as life. But it ain't about how hard ya hit. It's about how hard you can get it and keep moving forward. How much you can take and keep moving forward. That's how winning is done!
|
|
|
|
|
|
Current Student
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 410
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross) - Class of 2014
GMAT 1: 730 Q49 V39
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)
Followers: 6
Kudos [?]:
42
[0], given: 46
|
Re: Perimeter of triangle ABC. [#permalink]
11 Dec 2010, 09:19
Bunuel wrote: sriharimurthy wrote: Thanks Bunuel.
Though I just realized something. I considered the area given to be 40 by mistake. It is actually 20.
Although the logic will be same, the calculations will be harder since we will have to use the real value of \sqrt{3}. (no margin for approximations!)
Sorry for the mistake guys. However, as long as you understand the logic, it shouldn't matter. At least you'll know how to go about approaching such questions in the future!
Cheers.
Ps. Any trick for the calculations Bunuel? I would go backward. Let's assume the perimeter is 20. The largest area with given perimeter will have the equilateral triangle, so side=20/3. Let's calculate the area and if the area will be less than 20 it'll mean that perimeter must be more than 20. Area=s^2*\frac{\sqrt{3}}{4}=(\frac{20}{3})^2*\frac{\sqrt{3}}{4}=\frac{100*\sqrt{3}}{9}=~\frac{173}{9}<20Think this way is easier. \sqrt{3}\approx{1.73}. Thank you all for the explanations. I think I'm finally getting this!
_________________
Go Blue!
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 07 Feb 2010
Posts: 168
Followers: 1
Kudos [?]:
22
[0], given: 101
|
Re: Perimeter of triangle ABC. [#permalink]
17 Dec 2010, 06:44
for statement 2 u r using properties of equilateral triangle but no where in the q it is mentioned it is equilateral triangle
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12098
Followers: 1876
Kudos [?]:
10096
[1] , given: 959
|
Re: Perimeter of triangle ABC. [#permalink]
17 Dec 2010, 06:57
1
This post received
KUDOS
|
|
|
|
|
|
Manager
Joined: 07 Feb 2010
Posts: 168
Followers: 1
Kudos [?]:
22
[0], given: 101
|
Re: Perimeter of triangle ABC. [#permalink]
17 Dec 2010, 07:47
thanks bunuel got it
|
|
|
|
|
|
|
Re: Perimeter of triangle ABC.
[#permalink]
17 Dec 2010, 07:47
|
|
|
|
|
|
|
|
|
|
|
close
