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

It is currently 22 Oct 2014, 00:01

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

In, a Hemisphere igloo, an Eskimo’s head just touches the ro

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 19 Feb 2009
Posts: 77
Location: chennai
Followers: 3

Kudos [?]: 18 [0], given: 0

In, a Hemisphere igloo, an Eskimo’s head just touches the ro [#permalink] New post 06 Jun 2010, 18:41
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

49% (03:24) correct 51% (02:12) wrong based on 93 sessions
In, a Hemisphere igloo, an Eskimo’s head just touches the roof when he stands erect at the centre of the floor, but his son can play over an area of 9856 square units without stooping. If the Eskimo’s height is 65 units, what is his son’s height?

A. 25 units
B. 33 units
C. 35 units
D. 37 units
E. Insufficient data
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Mar 2014, 06:28, edited 2 times in total.
Renamed the topic and edited the question.
Intern
Intern
User avatar
Joined: 02 Apr 2010
Posts: 1
Location: Turkey
Followers: 0

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

Re: PS - Polygons [#permalink] New post 07 Jun 2010, 03:35
I have found the answer is 33

It takes a bit time, do you have any practical way?
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 422
WE 1: Business Development
Followers: 7

Kudos [?]: 35 [0], given: 161

GMAT ToolKit User
Re: PS - Polygons [#permalink] New post 17 Nov 2010, 22:37
hmm... i need to follow this one up...

Thanks for the question.
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23358
Followers: 3605

Kudos [?]: 28744 [1] , given: 2846

Re: PS - Polygons [#permalink] New post 18 Nov 2010, 05:32
1
This post received
KUDOS
Expert's post
lnarayanan wrote:
In,a Hemisphere igloo,an Eskimo’s head just touches the roof when he stands erect at the centre of the floor, but his son can play over an area of 9856 square units without stooping.If the Eskimo’s height is 65 units,What is his son’s height?
A) 25 units , B) 33 units , C) 35 units , D) 37 units ,E) Insufficient data


Look at the diagram below:
Attachment:
AngleSemicircle.gif
AngleSemicircle.gif [ 3.75 KiB | Viewed 3140 times ]
Now, the RADIUS of the igloo equals to the hight of the Eskimo, so R=65. As the child can play over an area of 9,856 square units then the radius of this playing are is: playing \ area=\pi{r^2}=9,856 --> r^2=\frac{9,856}{\pi} --> r\approx{56}. Thus the child's height will be H=\sqrt{R^2-r^2}=\sqrt{65^2-56^2}=33.

Answer: B.
_________________

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

Intern
Intern
User avatar
Joined: 27 Aug 2010
Posts: 30
Followers: 0

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

Re: PS - Polygons [#permalink] New post 20 Nov 2010, 14:31
Bunuel wrote:
lnarayanan wrote:
In,a Hemisphere igloo,an Eskimo’s head just touches the roof when he stands erect at the centre of the floor, but his son can play over an area of 9856 square units without stooping.If the Eskimo’s height is 65 units,What is his son’s height?
A) 25 units , B) 33 units , C) 35 units , D) 37 units ,E) Insufficient data


Look at the diagram below:
Attachment:
AngleSemicircle.gif
Now, the RADIUS of the igloo equals to the hight of the Eskimo, so R=65. As the child can play over an area of 9,856 square units then the radius of this playing are is: playing \ area=\pi{r^2}=9,856 --> r^2=\frac{9,856}{\pi} --> r\approx{56}. Thus the child's height will be H=\sqrt{R^2-r^2}=\sqrt{65^2-56^2}=33.

Answer: B.



Hi Bunnel ,
Got 2 doubts here
1) Aint the area should be playing \ area=\pi{r^2}/2 since its an hemisphere ?
2) While we are just concentrating on the right half should the area that of the quarter ?
M confused or may be i'm thinking in the wrong direction , Please explain .
_________________

This time , its my time .

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23358
Followers: 3605

Kudos [?]: 28744 [0], given: 2846

Re: PS - Polygons [#permalink] New post 21 Nov 2010, 00:52
Expert's post
girisshhh84 wrote:
Bunuel wrote:
lnarayanan wrote:
In,a Hemisphere igloo,an Eskimo’s head just touches the roof when he stands erect at the centre of the floor, but his son can play over an area of 9856 square units without stooping.If the Eskimo’s height is 65 units,What is his son’s height?
A) 25 units , B) 33 units , C) 35 units , D) 37 units ,E) Insufficient data


Look at the diagram below:
Attachment:
AngleSemicircle.gif
Now, the RADIUS of the igloo equals to the hight of the Eskimo, so R=65. As the child can play over an area of 9,856 square units then the radius of this playing are is: playing \ area=\pi{r^2}=9,856 --> r^2=\frac{9,856}{\pi} --> r\approx{56}. Thus the child's height will be H=\sqrt{R^2-r^2}=\sqrt{65^2-56^2}=33.

Answer: B.



Hi Bunnel ,
Got 2 doubts here
1) Aint the area should be playing \ area=\pi{r^2}/2 since its an hemisphere ?
2) While we are just concentrating on the right half should the area that of the quarter ?
M confused or may be i'm thinking in the wrong direction , Please explain .


I think you are just confused with the diagram:

Hemisphere is half of a sphere and the diagram gives the cross section of it. But the base of a hemisphere (the base of an igloo) is still a circle, so the playing area of the child is a circle limited by his height.
_________________

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
User avatar
Joined: 01 Nov 2010
Posts: 183
Location: Zürich, Switzerland
Followers: 2

Kudos [?]: 16 [0], given: 20

Re: PS - Polygons [#permalink] New post 21 Nov 2010, 13:15
Surface area of sphere is - 4 * pi (r)^2

Shoulden't area of hemisphere be -2 * pi (r)^2 ????
Manager
Manager
avatar
Joined: 21 Aug 2013
Posts: 113
Schools: ISB '15
Followers: 2

Kudos [?]: 10 [0], given: 54

Re: PS - Polygons [#permalink] New post 26 Mar 2014, 05:12
Bunuel wrote:
lnarayanan wrote:
In,a Hemisphere igloo,an Eskimo’s head just touches the roof when he stands erect at the centre of the floor, but his son can play over an area of 9856 square units without stooping.If the Eskimo’s height is 65 units,What is his son’s height?
A) 25 units , B) 33 units , C) 35 units , D) 37 units ,E) Insufficient data


Look at the diagram below:
Attachment:
AngleSemicircle.gif
Now, the RADIUS of the igloo equals to the hight of the Eskimo, so R=65. As the child can play over an area of 9,856 square units then the radius of this playing are is: playing \ area=\pi{r^2}=9,856 --> r^2=\frac{9,856}{\pi} --> r\approx{56}. Thus the child's height will be H=\sqrt{R^2-r^2}=\sqrt{65^2-56^2}=33.

Answer: B.



Hi Bunuel,
you can remove the approx sign.

9856/pi = 9856*7/22 = 56 exactly. :)
_________________

Veritas Prep - 650
MGMAT 1 590
MGMAT 2 640 (V48/Q31)

Please help the community by giving Kudos.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23358
Followers: 3605

Kudos [?]: 28744 [0], given: 2846

Re: PS - Polygons [#permalink] New post 26 Mar 2014, 06:38
Expert's post
seabhi wrote:
Bunuel wrote:
lnarayanan wrote:
In,a Hemisphere igloo,an Eskimo’s head just touches the roof when he stands erect at the centre of the floor, but his son can play over an area of 9856 square units without stooping.If the Eskimo’s height is 65 units,What is his son’s height?
A) 25 units , B) 33 units , C) 35 units , D) 37 units ,E) Insufficient data


Look at the diagram below:
Attachment:
AngleSemicircle.gif
Now, the RADIUS of the igloo equals to the hight of the Eskimo, so R=65. As the child can play over an area of 9,856 square units then the radius of this playing are is: playing \ area=\pi{r^2}=9,856 --> r^2=\frac{9,856}{\pi} --> r\approx{56}. Thus the child's height will be H=\sqrt{R^2-r^2}=\sqrt{65^2-56^2}=33.

Answer: B.



Hi Bunuel,
you can remove the approx sign.

9856/pi = 9856*7/22 = 56 exactly. :)


\pi=3.141592653589793238462643383279502884... (it goes on forever) is an irrational number, it cannot be represented as the ratio of two integers.

\frac{22}{7}=3.1428... is only an approximate value of \pi.

P.S. In that sense this is not a good quality question.
_________________

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

Intern
Intern
avatar
Joined: 22 Feb 2014
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 1

CAT Tests
Re: In, a Hemisphere igloo, an Eskimo’s head just touches the ro [#permalink] New post 14 May 2014, 20:37
9856 = 7*64*22. 22/7 is what we call as pi (at least an approximation of pi). So 9856/pi = 7*64*22/(22/7) = 7*7*64 = 3136. 3136 is 56^2. Easier than approximation.
Intern
Intern
avatar
Joined: 13 May 2014
Posts: 16
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: PS - Polygons [#permalink] New post 17 May 2014, 10:03
Bunuel wrote:
lnarayanan wrote:
In,a Hemisphere igloo,an Eskimo’s head just touches the roof when he stands erect at the centre of the floor, but his son can play over an area of 9856 square units without stooping.If the Eskimo’s height is 65 units,What is his son’s height?
A) 25 units , B) 33 units , C) 35 units , D) 37 units ,E) Insufficient data


Look at the diagram below:
Attachment:
AngleSemicircle.gif
Now, the RADIUS of the igloo equals to the hight of the Eskimo, so R=65. As the child can play over an area of 9,856 square units then the radius of this playing are is: playing \ area=\pi{r^2}=9,856 --> r^2=\frac{9,856}{\pi} --> r\approx{56}. Thus the child's height will be H=\sqrt{R^2-r^2}=\sqrt{65^2-56^2}=33.

Answer: B.


I had the solution to this problem in under a minute or so but couldn't actually compute the answer. Are we really supposed to be able to solve \sqrt{\frac{9,856}{\pi}} without a calculator? That seems like a stretch to me, but maybe I'm missing something... Is assuming \pi \approx \frac{22}{7} a standard assumption for this exam?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23358
Followers: 3605

Kudos [?]: 28744 [0], given: 2846

Re: PS - Polygons [#permalink] New post 18 May 2014, 00:01
Expert's post
GordonFreeman wrote:
Bunuel wrote:
lnarayanan wrote:
In,a Hemisphere igloo,an Eskimo’s head just touches the roof when he stands erect at the centre of the floor, but his son can play over an area of 9856 square units without stooping.If the Eskimo’s height is 65 units,What is his son’s height?
A) 25 units , B) 33 units , C) 35 units , D) 37 units ,E) Insufficient data


Look at the diagram below:
Attachment:
AngleSemicircle.gif
Now, the RADIUS of the igloo equals to the hight of the Eskimo, so R=65. As the child can play over an area of 9,856 square units then the radius of this playing are is: playing \ area=\pi{r^2}=9,856 --> r^2=\frac{9,856}{\pi} --> r\approx{56}. Thus the child's height will be H=\sqrt{R^2-r^2}=\sqrt{65^2-56^2}=33.

Answer: B.


I had the solution to this problem in under a minute or so but couldn't actually compute the answer. Are we really supposed to be able to solve \sqrt{\frac{9,856}{\pi}} without a calculator? That seems like a stretch to me, but maybe I'm missing something... Is assuming \pi \approx \frac{22}{7} a standard assumption for this exam?


As I've written above this is not a proper GMAT question because we need to approximate \pi to get the answer, while the question does not ask about approximate height. GMAT would never do that.

As for \pi \approx \frac{22}{7}: this is a good/standard approximation for some problems asking for an approximate answer.
_________________

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

Intern
Intern
avatar
Joined: 13 May 2014
Posts: 16
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: PS - Polygons [#permalink] New post 18 May 2014, 16:39
Bunuel wrote:
I had the solution to this problem in under a minute or so but couldn't actually compute the answer. Are we really supposed to be able to solve \sqrt{\frac{9,856}{\pi}} without a calculator? That seems like a stretch to me, but maybe I'm missing something... Is assuming \pi \approx \frac{22}{7} a standard assumption for this exam?


As I've written above this is not a proper GMAT question because we need to approximate \pi to get the answer, while the question does not ask about approximate height. GMAT would never do that.

As for \pi \approx \frac{22}{7}: this is a good/standard approximation for some problems asking for an approximate answer.[/quote]

Are we expected to know the square root of 3,136 is 56 off the top of our heads as well? I'm just trying to get a sense for what I need to memorize.
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4876
Location: Pune, India
Followers: 1152

Kudos [?]: 5353 [0], given: 165

Re: PS - Polygons [#permalink] New post 18 May 2014, 22:30
Expert's post
GordonFreeman wrote:
Bunuel wrote:
I had the solution to this problem in under a minute or so but couldn't actually compute the answer. Are we really supposed to be able to solve \sqrt{\frac{9,856}{\pi}} without a calculator? That seems like a stretch to me, but maybe I'm missing something... Is assuming \pi \approx \frac{22}{7} a standard assumption for this exam?


As I've written above this is not a proper GMAT question because we need to approximate \pi to get the answer, while the question does not ask about approximate height. GMAT would never do that.

As for \pi \approx \frac{22}{7}: this is a good/standard approximation for some problems asking for an approximate answer.

Are we expected to know the square root of 3,136 is 56 off the top of our heads as well? I'm just trying to get a sense for what I need to memorize.


No. There is very little memorization that is expected from you. But what is expected is that you will reduce the calculations you need to do using reasoning.

If such a question does come in GMAT, the number will be and easier than 9856. Also, you can easily solve with 9856 too.

r^2 = 9856/pi = 9856*7/22

r must be an integer otherwise this calculation will become far too cumbersome for GMAT. So 9856 will be completely divisible by 22.
Also, 9856 must have 7 as a factor since perfect squares have powers of prime factors in pairs.
So let's try to split 9856 into factors. We already know that it must have 7 as a factor and 11 as a factor (to be divisible by 22)

9856 = 7*1408 = 7*11*128 = 7*11*2^7 (you must know that 2^7 = 128)

r^2 = \frac{7*11*2^7}{2*11} = 7*2^3 = 56

Again, H = \sqrt{65^2 - 56^2} = \sqrt{(65+56)(65 - 56)} = \sqrt{121*9} = 11*3 = 33
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: PS - Polygons   [#permalink] 18 May 2014, 22:30
    Similar topics Author Replies Last post
Similar
Topics:
1 I will just ignore AWA and head to the Q&V. Comments?!! deveinn 6 12 Dec 2011, 03:50
2 Experts publish their posts in the topic In, a Hemisphere igloo, an Eskimo’s head just touches the ro lnarayanan 13 06 Jun 2010, 18:41
17 Keep in touch agold 29 21 Nov 2008, 22:00
Q. Just when bankruptcy reform appears headed for a certain mohish 8 25 Oct 2005, 08:45
Eskimo praveen_rao7 6 05 Mar 2005, 23:22
Display posts from previous: Sort by

In, a Hemisphere igloo, an Eskimo’s head just touches the ro

  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®.