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

It is currently 23 Jul 2014, 12:53

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

m22#30

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18705
Followers: 3236

Kudos [?]: 22277 [3] , given: 2611

Re: m22#30 [#permalink] New post 25 Apr 2012, 08:07
3
This post received
KUDOS
Expert's post
harshavmrg wrote:
Bunuel....Can u please explain the solution..( both options A and B)... i am quite confused about this problem of how is A sufficient and how is B insufficient


A rectangle is inscribed in a circle of radius 5. Is the area of the rectangle bigger than 48 ?

Look at the diagram below:
Attachment:
Rectangle.png
Rectangle.png [ 15.39 KiB | Viewed 5561 times ]

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. Since a rectangle is made of two right triangles then a rectangle inscribed in a circle must have its diagonal as the diameter of the circle.

Given: radius=5 --> diameter=diagonal=10. Question: area=ab=?, where a and b are the sides of the rectangle.

(1) The ratio of the lengths of sides of the rectangle is 3:4 --> \frac{a}{b}=\frac{3x}{4x}, for some positive multiple x. So, diagonal^2=a^2+b^2=(3x)^2+(4x)^2 --> 100=9x^2+16x^2 --> x=2 --> a=3x=6 and b=4x=8 --> area=ab=6*8=48. Sufficient.

Alternately, even not calculating, one can spot that since hypotenuse (diameter) is 10 and the legs are in the ratio of 3 to 4 then we have 6-8-10 right triangle (Pythagorean Triple).

(2) The difference between the lengths of sides of the rectangle is smaller than 3 --> b-a<3 --> square both sides: b^2-2ab+a^2<9. Now, since diagonal=10^2=a^2+b^2 then 100-2ab<9 --> ab>45.5. So we have that area=ab>45.5, hence the are may or may not be more than 48. Not sufficient.

Answer: A.

Hope it's clear.

_________________

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

Senior Manager
Senior Manager
avatar
Joined: 08 Jun 2010
Posts: 397
Location: United States
Concentration: General Management, Finance
GMAT 1: 680 Q50 V32
Followers: 2

Kudos [?]: 55 [0], given: 13

GMAT Tests User
Re: m22#30 [#permalink] New post 04 Jul 2012, 00:52
My attempt at a more elegant solution :)

So, we can rephrase the question as
75 (Approx 25pi) > xy> 48?

1) SUFFICIENT
Let's try multiples of the ratio of 3:4
(3,4) -- FALSE
(6,8) -- FALSE
(9,12) --FALSE
We can see that at any multiple the value the statement doesn't hold true.

2) INSUFFICIENT
Given: x-y<3, we can find two values
1) where x-y<3 and xy is greater than 75 e.g. 9,10
2) where x-y<3 and xy is in between 75 (Approx 25pi) > xy> 48 , e.g. 8,8
Manager
Manager
avatar
Joined: 24 Feb 2013
Posts: 105
GMAT 1: 660 Q47 V35
GMAT 2: 690 Q46 V38
GMAT 3: 680 Q46 V37
GMAT 4: 680 Q45 V39
GMAT 5: 760 Q48 V47
GPA: 3.97
Followers: 0

Kudos [?]: -8 [0], given: 45

Re: m22#30 [#permalink] New post 19 Mar 2013, 12:09
Quote:
S2: b - a < 3
Squaring both the sides of the inequality, gives:
a^2 + b^2 - 2ab < 9 => 100 - 2ab < 9
Solving the inequality gives: ab > 45.5
Therefore, ab > 48 may or may not be true.


I need help- why does the inequality sign flip? Why don't we add 2ab and subtract 9 to both sides of 100 - 2ab + 2an -9 < 9 + 2ab -9 = 91 < 2AB, then divide by positive 2 = 45.5 < AB?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18705
Followers: 3236

Kudos [?]: 22277 [0], given: 2611

Re: m22#30 [#permalink] New post 19 Mar 2013, 13:36
Expert's post
shanek wrote:
Quote:
S2: b - a < 3
Squaring both the sides of the inequality, gives:
a^2 + b^2 - 2ab < 9 => 100 - 2ab < 9
Solving the inequality gives: ab > 45.5
Therefore, ab > 48 may or may not be true.


I need help- why does the inequality sign flip? Why don't we add 2ab and subtract 9 to both sides of 100 - 2ab + 2an -9 < 9 + 2ab -9 = 91 < 2AB, then divide by positive 2 = 45.5 < AB?


Aren't you getting the same result?

Anyway, check here for a solution: m22-73309-20.html#p1078258

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

Manager
Manager
avatar
Joined: 24 Feb 2013
Posts: 105
GMAT 1: 660 Q47 V35
GMAT 2: 690 Q46 V38
GMAT 3: 680 Q46 V37
GMAT 4: 680 Q45 V39
GMAT 5: 760 Q48 V47
GPA: 3.97
Followers: 0

Kudos [?]: -8 [0], given: 45

Re: m22#30 [#permalink] New post 20 Mar 2013, 03:57
Bunuel wrote:
shanek wrote:
Quote:
S2: b - a < 3
Squaring both the sides of the inequality, gives:
a^2 + b^2 - 2ab < 9 => 100 - 2ab < 9
Solving the inequality gives: ab > 45.5
Therefore, ab > 48 may or may not be true.


I need help- why does the inequality sign flip? Why don't we add 2ab and subtract 9 to both sides of 100 - 2ab + 2an -9 < 9 + 2ab -9 = 91 < 2AB, then divide by positive 2 = 45.5 < AB?


Aren't you getting the same result?

Anyway, check here for a solution: m22-73309-20.html#p1078258

Hope it helps.


Wow. I guess your tests really are hard.. after 2 of them I went full retard. I was staring at this for an hour. After a good night's sleep, it's REALLY obvious, and I'm embarrassed.

Thank you Bunuel.. awesome website.
Intern
Intern
avatar
Joined: 11 Jan 2010
Posts: 38
Followers: 1

Kudos [?]: 50 [0], given: 6

Re: m22#30 [#permalink] New post 20 Mar 2013, 04:37
In regards to question about flipping the sign on the inequality, the below is how I look at it:

Taking from inequality: 100 - 2ab < 9
Subtract 100 from both sides of inequality:
100 - 2ab < 9 - 100
=> -2ab < -91

Divide 2 from both sides of inequality:
(-2ab) / 2 < (-91) / 2
=> -ab < -45.5

Now, this is where the flipping of the inequality sign comes into play. The rule is that when you change the arithmetic sign from negative to positive in an inequality, you should flip the sign of the inequality.

=> ab > 45.5

Hope this answers your question. Cheers!! Happy GMATing!!! :)
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 15 Jun 2012
Posts: 992
Location: United States
Followers: 112

Kudos [?]: 1094 [0], given: 118

Re: m22#30 [#permalink] New post 21 Mar 2013, 21:55
vshrivastava wrote:
Suppose sides of the ractangle are a and b.

S2: b - a < 3
Squaring both the sides of the inequality, gives:
a^2 + b^2 - 2ab < 9 => 100 - 2ab < 9
Solving the inequality gives: ab > 45.5
Therefore, ab > 48 may or may not be true.

Result: S2 is NOT sufficient to answer the question.

My answer is A.


Vshrivastava,

Even though I got this question correct, but I do like the way you prove the second statement insufficient. Thanks so much.

_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMV Chief of Design.

Intern
Intern
avatar
Joined: 03 Sep 2011
Posts: 18
Followers: 0

Kudos [?]: 3 [0], given: 4

GMAT ToolKit User
Re: m22#30 [#permalink] New post 31 Mar 2013, 17:50
I often find myself doing unecessary calculations in DS. In my opinion working on this is the best way to get more comfortable with the time. On this question, for statement 1, wouldn't it suffice to notice that there is only one possible rectangle with sides of ratio 2:3 that can fit inside a circle of radius 5? What I mean is everyone in this thread calculated that the area of this rectangle is 48 but isn't this unecessary? We basicaly don't really care if it's 48, more than 48 or less than 48.. Am I making a mistake somewhere? thank you
Intern
Intern
avatar
Joined: 11 Jan 2010
Posts: 38
Followers: 1

Kudos [?]: 50 [0], given: 6

Re: m22#30 [#permalink] New post 31 Mar 2013, 18:45
I've always believed that the DS problems are a lot about developing intuition on the sufficiency test for the given statements. One who can develop such intuition can sure gain on time; but one might give away on accuracy. For example, I'd be careful while evaluating sufficiency in problems involving inequalities and would perform necessary calculations before making up my mind on sufficiency. Hope this helps!!
Senior Manager
Senior Manager
avatar
Joined: 07 Sep 2010
Posts: 340
Followers: 2

Kudos [?]: 93 [0], given: 136

Re: m22#30 [#permalink] New post 06 May 2013, 04:52
Hi Experts,

The Official Explanation for Statement B
says that -
The difference between the lengths of sides of the rectangle is smaller than 3. Given that b−a<3. Square both sides: b2−2ab+a2<9. Now, since diagonal=102=a2+b2 then 100−2ab<9, soab>45.5. So we have that area=ab>45.5, hence the area may or may not be more than 48. Not sufficient

My doubt is -Can we Square the given Inequality(b−a<3), since rule says that until and unless you are sure about both terms being positive you cannot square the Inequality. How can we be sure that the LHS or RHS is positive. Please explain.

Regards,
H

_________________

+1 Kudos me, Help me unlocking GMAT Club Tests

Intern
Intern
avatar
Joined: 20 Mar 2012
Posts: 22
Location: United States
Concentration: General Management, Marketing
GMAT 1: 700 Q49 V35
GPA: 3.25
WE: Operations (Military & Defense)
Followers: 0

Kudos [?]: 7 [0], given: 68

Re: m22#30 [#permalink] New post 01 Jul 2013, 08:09
Bunuel wrote:
sahilkhurana06 wrote:
Answer is D (Correct me if I am wrong)

Statement 1 : Everybody knows that this is sufficient.
Statement 2 : It says that the difference between the lengths of sides of the rectangle is smaller than 3,so that means l-b < 3..Also it has a fact that the diagonal of the rectangle is 10 (since radius of circle is 5).Now,considering these values (l^2 + b^2 = 100 and l-b<3),we have only one possibility when the diagonal can be of 10 units i.e. when we have sides 8 and 6.Hence,this statement is also sufficient to answer.

Let me know what you guys think....


Statement (2) is not sufficient, see algebraic solutions on previous page or consider the following examples:

If a=8 and b=6 (a-b=2<3 and a^2+b^2=100) then area=ab=48 and the answer to the question "is area>48" is NO;

If a=b=\sqrt{50} (a-b=0<3 and a^2+b^2=100) then area=ab=50 and the answer to the question "is area>48" is YES. Note that in this case inscribed figure is square, which is a special type of rectangle.

Two different answers not sufficient.

Answer: A.

I think that the problem with your solution is that you assumed with no ground for it that the lengths of the sides of the rectangle are integers.

Hope it's clear.


Bunuel, I understand the solution given in your other explanation. Thanks for the help. My question is on this first explination. How do we get a=b=\sqrt{50}? Is it simply because a^2+b^2=100...I think I figured it out as I was typing this, but is that correct? I was originally trying to draw a connection to the radius and the sides of the square (25+25...) Anyway.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18705
Followers: 3236

Kudos [?]: 22277 [1] , given: 2611

Re: m22#30 [#permalink] New post 01 Jul 2013, 08:30
1
This post received
KUDOS
Expert's post
usmabama wrote:
Bunuel wrote:
sahilkhurana06 wrote:
Answer is D (Correct me if I am wrong)

Statement 1 : Everybody knows that this is sufficient.
Statement 2 : It says that the difference between the lengths of sides of the rectangle is smaller than 3,so that means l-b < 3..Also it has a fact that the diagonal of the rectangle is 10 (since radius of circle is 5).Now,considering these values (l^2 + b^2 = 100 and l-b<3),we have only one possibility when the diagonal can be of 10 units i.e. when we have sides 8 and 6.Hence,this statement is also sufficient to answer.

Let me know what you guys think....


Statement (2) is not sufficient, see algebraic solutions on previous page or consider the following examples:

If a=8 and b=6 (a-b=2<3 and a^2+b^2=100) then area=ab=48 and the answer to the question "is area>48" is NO;

If a=b=\sqrt{50} (a-b=0<3 and a^2+b^2=100) then area=ab=50 and the answer to the question "is area>48" is YES. Note that in this case inscribed figure is square, which is a special type of rectangle.

Two different answers not sufficient.

Answer: A.

I think that the problem with your solution is that you assumed with no ground for it that the lengths of the sides of the rectangle are integers.

Hope it's clear.


Bunuel, I understand the solution given in your other explanation. Thanks for the help. My question is on this first explination. How do we get a=b=\sqrt{50}? Is it simply because a^2+b^2=100...I think I figured it out as I was typing this, but is that correct? I was originally trying to draw a connection to the radius and the sides of the square (25+25...) Anyway.


Yes. a=8 and b=6 AND a=b=\sqrt{50} are just examples to show that (2) is not sufficient. Notice that both satisfy a-b=2 and a^2+b^2=100.

_________________

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

Manager
Manager
avatar
Joined: 11 Dec 2010
Posts: 115
WE: Consulting (Consulting)
Followers: 4

Kudos [?]: 23 [0], given: 50

Re: m22#30 [#permalink] New post 23 Jul 2013, 22:31
Another approach for Option B: Rectangle with largest area is square. So if square were to be fit in the circle, the area would be 50 ((5\sqrt{2})^2). With 8 and 6 as the sides (as 10 is the radius), the area would be 48. The difference in lengths here is less than 2. If the difference were to increase (suppose 2.5), the area would be below 48. So according to this option, it can be above or below 48.

@Bunuel - Is my approach correct?
1 KUDOS received
Intern
Intern
avatar
Status: At the end all are winners, Some just take a little more time to win.
Joined: 08 Oct 2013
Posts: 23
Location: India
Concentration: Finance, Accounting
GMAT Date: 11-20-2013
GPA: 3.97
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 7 [1] , given: 45

Re: m22#30 [#permalink] New post 26 Oct 2013, 05:29
1
This post received
KUDOS
Why would we need any of the two statements. The question itself is sufficient:

The rectangle is inscribed in the circle of radius 5; so diameter would be 10: This has to be the diagonal of the inscribed rectangle.

The sides has to be 6 & 8 and area would be equal to 48.

Correct me if i am missing something round here
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18705
Followers: 3236

Kudos [?]: 22277 [1] , given: 2611

Re: m22#30 [#permalink] New post 27 Oct 2013, 05:12
1
This post received
KUDOS
Expert's post
amkabdul wrote:
Why would we need any of the two statements. The question itself is sufficient:

The rectangle is inscribed in the circle of radius 5; so diameter would be 10: This has to be the diagonal of the inscribed rectangle.

The sides has to be 6 & 8 and area would be equal to 48.

Correct me if i am missing something round here


You assume with no ground for it that the lengths of the sides are integers. Knowing that hypotenuse equals to 10 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple - 6:8:10. Or in other words: if a^2+b^2=10^2 DOES NOT mean that a=6 and b=8, certainly this is one of the possibilities but definitely not the only one. In fact a^2+b^2=10^2 has infinitely many solutions for a and b and only one of them is a=6 and b=8.

For example: a=1 and b=\sqrt{99} or a=2 and b=\sqrt{96} ...

Hope it's clear.

_________________

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

Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 408
Followers: 2

Kudos [?]: 48 [0], given: 82

CAT Tests
Re: m22#30 [#permalink] New post 27 Feb 2014, 01:04
Bunuel.. There was one question in gmat club tests, I dont remember which question it was! In which it was mentioned that rectangle is inscribed in circle.. bt OE was , its not neccessary rectangle wud cross through radius of circle or it can touch any point of circle..

Thats y i chose E for this question. because i thought rectangle inscribed in circle mean it can touch any point of circle.

_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Re: m22#30   [#permalink] 27 Feb 2014, 01:04
Display posts from previous: Sort by

m22#30

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   [ 36 posts ] 



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®.