GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Oct 2018, 07:52

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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 20 Feb 2009
Posts: 64
Location: chennai
In, a Hemisphere igloo, an Eskimo’s head just touches the ro  [#permalink]

Show Tags

New post Updated on: 26 Mar 2014, 07:28
3
19
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

49% (02:54) correct 51% (02:42) wrong based on 267 sessions

HideShow timer Statistics

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

Originally posted by lnarayanan on 06 Jun 2010, 19:41.
Last edited by Bunuel on 26 Mar 2014, 07:28, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
In, a Hemisphere igloo, an Eskimo’s head just touches the ro  [#permalink]

Show Tags

New post 18 Nov 2010, 06:32
4
4
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:

Image

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.

Attachment:
AngleSemicircle.gif
AngleSemicircle.gif [ 3.75 KiB | Viewed 8671 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
User avatar
Joined: 27 Aug 2010
Posts: 27
Re: PS - Polygons  [#permalink]

Show Tags

New post 20 Nov 2010, 15:31
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 .

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re: PS - Polygons  [#permalink]

Show Tags

New post 21 Nov 2010, 01:52
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
Joined: 01 Nov 2010
Posts: 129
Location: Zürich, Switzerland
Re: PS - Polygons  [#permalink]

Show Tags

New post 21 Nov 2010, 14:15
Surface area of sphere is - 4 * pi (r)^2

Shoulden't area of hemisphere be -2 * pi (r)^2 ????
Manager
Manager
avatar
Joined: 22 Aug 2013
Posts: 80
Schools: ISB '15
Re: PS - Polygons  [#permalink]

Show Tags

New post 26 Mar 2014, 06:12
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.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re: PS - Polygons  [#permalink]

Show Tags

New post 26 Mar 2014, 07:38
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 22 Feb 2014
Posts: 30
Reviews Badge
Re: In, a Hemisphere igloo, an Eskimo’s head just touches the ro  [#permalink]

Show Tags

New post 14 May 2014, 21:37
1
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
Re: PS - Polygons  [#permalink]

Show Tags

New post 17 May 2014, 11:03
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?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50058
Re: PS - Polygons  [#permalink]

Show Tags

New post 18 May 2014, 01:01
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 13 May 2014
Posts: 16
Re: PS - Polygons  [#permalink]

Show Tags

New post 18 May 2014, 17:39
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.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8418
Location: Pune, India
Re: PS - Polygons  [#permalink]

Show Tags

New post 18 May 2014, 23:30
2
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8539
Premium Member
Re: In, a Hemisphere igloo, an Eskimo’s head just touches the ro  [#permalink]

Show Tags

New post 26 Mar 2018, 21:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: In, a Hemisphere igloo, an Eskimo’s head just touches the ro &nbs [#permalink] 26 Mar 2018, 21:57
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.