Find all School-related info fast with the new School-Specific MBA Forum

It is currently 02 Oct 2014, 00:30

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the perimeter of rectangle R?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1318
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 57

Kudos [?]: 490 [0], given: 157

GMAT ToolKit User
What is the perimeter of rectangle R? [#permalink] New post 26 Jun 2010, 06:58
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:40) correct 22% (00:55) wrong based on 64 sessions
What is the perimeter of rectangle R?

(1) The area of rectangle R is 60.

(2) The length of a diagonal of rectangle R is 13.
[Reveal] Spoiler: OA

_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Get the best GMAT Prep Resources with GMAT Club Premium Membership


Last edited by Bunuel on 20 Jul 2012, 03:31, edited 1 time in total.
Edited the question and added the OA.
1 KUDOS received
Ms. Big Fat Panda
Ms. Big Fat Panda
User avatar
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1856
Concentration: Social Entrepreneurship, Organizational Behavior
Followers: 340

Kudos [?]: 1395 [1] , given: 194

GMAT ToolKit User
Re: One more geometry [#permalink] New post 26 Jun 2010, 07:24
1
This post received
KUDOS
I think the answer is C.

Statement 1: Area = 60

This implies that l*b = 60 where l and b are length and breadth respectively. This could mean a million possibilities. So insufficient and we are down to BCE.

Statement 2: Length of diagonal = 13.

This implies that \sqrt{l^2 + b^2} = 13

So at this point, I am a little confused about one tiny detail.

Scenario 1: We can assume that all sides of the rectangle are integers, in which case Statement alone is sufficient since the only two integers whose sum of squares is 13 are 12 and 5. So we are done.

Scenario 2: We cannot assume that all sides are integers, in which case statement two is insufficient and we use statement 1 with statement 2 to figure out the answer.

b = \frac{60}{l}

Substituting that into statement 2, we get:

\sqrt{l^2 + (60/l)^2} = 13

This can be solved for a value of l and hence we get C as our answer. What's the OA?

Last edited by whiplash2411 on 26 Jun 2010, 19:54, edited 1 time in total.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23066
Followers: 3542

Kudos [?]: 27342 [0], given: 2734

Re: One more geometry [#permalink] New post 26 Jun 2010, 08:23
Expert's post
Hussain15 wrote:
What is the perimeter of rectangle R?

(1) The area of rectangle R is 60.

(2) The length of a diagonal of rectangle R is 13.

I wanna discuss this one in detail.


Let the sides be x and y. Question: P=2(x+y)=?

(1) area=xy=60. Clearly insufficient.
(2) x^2+y^2=13^2=169. Also insufficient.

(1)+(2) Square P --> P^2=4(x+y)^2=4(x^2+2xy+y^2) as from (1) xy=60 and from (2) x^2+y^2=169, then P^2=4(x^2+2xy+y^2)=4(169+120)=4*289 --> P=\sqrt{4*289}=2*17=34. Sufficient.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1318
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 57

Kudos [?]: 490 [0], given: 157

GMAT ToolKit User
Re: One more geometry [#permalink] New post 26 Jun 2010, 09:21
OA is "C", but why??? It should be "B". We know the 13-12-5 principle. If hypotenuse is 13, then the other two sides can be determined.
Why not "B"?????

Posted from my mobile device Image
_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3571
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 365

Kudos [?]: 1809 [0], given: 358

GMAT ToolKit User Premium Member
Re: One more geometry [#permalink] New post 26 Jun 2010, 09:27
Expert's post
Hussain15 wrote:
OA is "C", but why??? It should be "B". We know the 13-12-5 principle. If hypotenuse is 13, then the other two sides can be determined.
Why not "B"?????


What about 13-\frac{13}{\sqrt{2}}-\frac{13}{\sqrt{2}} ?
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23066
Followers: 3542

Kudos [?]: 27342 [3] , given: 2734

Re: One more geometry [#permalink] New post 26 Jun 2010, 09:45
3
This post received
KUDOS
Expert's post
Hussain15 wrote:
OA is "C", but why??? It should be "B". We know the 13-12-5 principle. If hypotenuse is 13, then the other two sides can be determined.
Why not "B"?????

Posted from my mobile device Image


5-12-13 is a Pythagorean triple. What is Pythagorean triple?

Triangles that have their sides in the ratio of whole numbers (integers) are called Pythagorean Triples. The smallest one is 3:4:5. If you multiply the sides by any number, the result will still be a right triangle whose sides are in the ratio 3:4:5. For example 6, 8, and 10.

A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. There are 16 primitive Pythagorean triples with c ≤ 100:
(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17) (9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65) (36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97).

BUT:

Knowing that hypotenuse equals to 13 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple - 5:12:13. Or in other words: if a^2+b^2=13^2 DOES NOT mean that a=5 and b=12, certainly this is one of the possibilities but definitely not the only one. In fact a^2+b^2=13^2 has infinitely many solutions for a and b and only one of them is a=5 and b=12.

For example: a=1 and b=\sqrt{168} or a=2 and b=\sqrt{165} or a=4 and b=\sqrt{153} or a=2.5 and b=\sqrt{162.75}...

So knowing that the diagonal of a rectangle (hypotenuse) equals to one of the Pythagorean triple hypotenuse value is not sufficient to calculate the sides of this rectangle.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 180

Kudos [?]: 957 [0], given: 235

Reviews Badge
Re: One more geometry [#permalink] New post 26 Jun 2010, 09:46
No this is wrong. a^2+b^2 = 13^2 holds true for many values of (a,b)

You cannot deduce a and b to be 12,5

what if a^2 = 6 and b^=7, it was not even given that they have integral value. Even if it was given a and b are integers you still have to think whether any integral pair a,b exists which is unique.

no doubt 2+2 = 4, but you can not deduce 4 = 2+2 only...it can be 3+1....This reasoning will help you in CR - cause and effect.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Intern
avatar
Joined: 24 Nov 2008
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: One more geometry [#permalink] New post 26 Jun 2010, 16:24
Hussain15 wrote:
OA is "C", but why??? It should be "B". We know the 13-12-5 principle. If hypotenuse is 13, then the other two sides can be determined.
Why not "B"?????

Posted from my mobile device Image


ans c
I am no Math Genius ..but if you deduce this a^2 +b^2=C^2..then it doesn't mean that triplet a,b, c are pythgorean triplet.

But if a right angle triangle is given ..then yes a,b,c satisfy pythagoras theorem and if c is given then you can find a and b.
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1318
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 57

Kudos [?]: 490 [0], given: 157

GMAT ToolKit User
Re: One more geometry [#permalink] New post 27 Jun 2010, 03:51
Senior Manager
Senior Manager
User avatar
Joined: 25 Feb 2010
Posts: 459
Followers: 3

Kudos [?]: 35 [0], given: 5

Re: One more geometry [#permalink] New post 28 Jun 2010, 06:37
Hussain15 wrote:
OA is "C", but why??? It should be "B". We know the 13-12-5 principle. If hypotenuse is 13, then the other two sides can be determined.
Why not "B"?????

Posted from my mobile device Image


Dude,

Not Every Red car is Ferrari ... :)

Just kidding... 8-)

So every triplet is not 13-12-5
_________________

GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...

Intern
Intern
avatar
Joined: 13 Jun 2008
Posts: 21
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: One more geometry [#permalink] New post 28 Jun 2010, 10:36
When can you use the x:x:x√2 ratio for triangles, i thought you could on a 90 45 45 triangle?
Re: One more geometry   [#permalink] 28 Jun 2010, 10:36
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic What is the perimeter of rectangle ABCD ? jamifahad 8 29 Sep 2011, 05:05
1 Experts publish their posts in the topic Is the value of the perimeter of rectangle R greater than guygmat 3 19 Jun 2011, 22:20
1 What is the perimeter of the rectangle attached herewith? bhandariavi 2 14 Feb 2011, 19:02
The perimeter of square S and rectangle R are equal if the myc2004 2 24 Apr 2006, 17:20
1 Experts publish their posts in the topic If p is the perimeter of rectangle Q, what is the value of omomo 7 13 Nov 2005, 09:41
Display posts from previous: Sort by

What is the perimeter of rectangle R?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.