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

It is currently 14 Nov 2018, 03:23

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

Point a is the center of both a circle and a square. The circle, which

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50579
Point a is the center of both a circle and a square. The circle, which  [#permalink]

Show Tags

New post 25 Jun 2015, 03:20
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (02:48) correct 33% (02:50) wrong based on 128 sessions

HideShow timer Statistics

Image

Point a is the center of both a circle and a square. The circle, which is fully shown above, is inscribed in the square and the circle is tangent on all sides with the square, which is only partially shown and has both the x-axis and the y-axis as sides. The origin (0,0) is the bottom-left corner of the square and the line DE is a diagonal of the square. If the x-coordinate of point a is \(x_1\), what is the area of the gray shaded region between the circle and the origin (0,0)?

A) \(0.25(x_1)^2(4 - \pi)\)
B) \((x_1)^2 - (x_1)^2\pi\)
C) \(0.25(2(x_1)^2 - (x_1)^2)\pi)\)
D) \(4(x_1)^2 - (x_1)^2\pi\)
E) \((x_1)^2 - (x_1)^2*0.5\pi\)

Source: Platinum GMAT
Kudos for a correct solution.

Attachment:
00023-1.gif
00023-1.gif [ 5.84 KiB | Viewed 3375 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

Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 846
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Point a is the center of both a circle and a square. The circle, which  [#permalink]

Show Tags

New post 25 Jun 2015, 03:57
It's a pity that this task has no real value which could have been ballparked. Since we have this little shaded region which we need to find, it must be a quarter of something. Because within the square there are 4 of the same regions like the one which is shaded. So we need 1/4(the square - the circle). For me only answer choice C fits. That's my approach on how I would have done it ... no sure thing.

Answer Choice C
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2698
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: Point a is the center of both a circle and a square. The circle, which  [#permalink]

Show Tags

New post 25 Jun 2015, 05:10
2
[quote="Bunuel"]Image

Point a is the center of both a circle and a square. The circle, which is fully shown above, is inscribed in the square and the circle is tangent on all sides with the square, which is only partially shown and has both the x-axis and the y-axis as sides. The origin (0,0) is the bottom-left corner of the square and the line DE is a diagonal of the square. If the x-coordinate of point a is \(x_1\), what is the area of the gray shaded region between the circle and the origin (0,0)?

A) \(0.25(x_1)^2(4 - \pi)\)
B) \((x_1)^2 - (x_1)^2\pi\)
C) \(0.25(2(x_1)^2 - (x_1)^2)\pi)\)
D) \(4(x_1)^2 - (x_1)^2\pi\)
E) \((x_1)^2 - (x_1)^2*0.5\pi\)

Source: Platinum GMAT
Kudos for a correct solution.



Answer: Option

Please find the solution with diagram as attached.
Attachments

File comment: www.GMATinsight.com
Soltuion 1.jpg
Soltuion 1.jpg [ 177.36 KiB | Viewed 2663 times ]


_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2698
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: Point a is the center of both a circle and a square. The circle, which  [#permalink]

Show Tags

New post 25 Jun 2015, 05:15
1
reto wrote:
It's a pity that this task has no real value which could have been ballparked. Since we have this little shaded region which we need to find, it must be a quarter of something. Because within the square there are 4 of the same regions like the one which is shaded. So we need 1/4(the square - the circle). For me only answer choice C fits. That's my approach on how I would have done it ... no sure thing.

Answer Choice C


According to Option C, \(\pi\) is factor of both area of Square and Area of Circle and that's where this option proves to be wrong as Area of Square will not be a multiple of \(\pi\) for sure.

But Option C might have misled you because there is a closing bracket after \(\pi\) whereas that has no open side :wink:
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Queens MBA Thread Master
avatar
Joined: 24 Oct 2012
Posts: 170
Concentration: Leadership, General Management
Re: Point a is the center of both a circle and a square. The circle, which  [#permalink]

Show Tags

New post 26 Jun 2015, 06:48
1
Bunuel wrote:
Image

Point a is the center of both a circle and a square. The circle, which is fully shown above, is inscribed in the square and the circle is tangent on all sides with the square, which is only partially shown and has both the x-axis and the y-axis as sides. The origin (0,0) is the bottom-left corner of the square and the line DE is a diagonal of the square. If the x-coordinate of point a is \(x_1\), what is the area of the gray shaded region between the circle and the origin (0,0)?

A) \(0.25(x_1)^2(4 - \pi)\)
B) \((x_1)^2 - (x_1)^2\pi\)
C) \(0.25(2(x_1)^2 - (x_1)^2)\pi)\)
D) \(4(x_1)^2 - (x_1)^2\pi\)
E) \((x_1)^2 - (x_1)^2*0.5\pi\)

Source: Platinum GMAT
Kudos for a correct solution.

Attachment:
00023-1.gif


From the description :
Radius of Circle = x1
Side of square = 2 x1

Area of circle = \pi \((x1)^ 2\)
Area of Square = \((2X1) ^ 2\)

Area of Square- Area of circle = 4 * area of shaded region = \((x_1)^2(4 - \pi)\)
Hence Area of shaded region = \(0.25(x_1)^2(4 - \pi)\)
Option A
Manager
Manager
avatar
B
Joined: 26 Dec 2012
Posts: 146
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
CAT Tests
Re: Point a is the center of both a circle and a square. The circle, which  [#permalink]

Show Tags

New post 26 Jun 2015, 09:13
Required value = 1/4( area of square-area of circle)
Point a =x1; therefore diagonal of square = 2x1
Side of square =root2 x1 ; therefore area of square =2x1^2
Radius of circle = side of square/2=x1/root2
Area of circle =pir *x1^2/2
Therefore putting area value in first equation we get =1/8 * (4-pie) *x1^2

Hence answer is A
Thanks,
Current Student
avatar
Joined: 22 Apr 2015
Posts: 46
Location: United States
GMAT 1: 620 Q46 V27
GPA: 3.86
Re: Point a is the center of both a circle and a square. The circle, which  [#permalink]

Show Tags

New post 26 Jun 2015, 18:35
Im going with A.

x=x1

(A(Square)-A(Cirlce))/4
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50579
Re: Point a is the center of both a circle and a square. The circle, which  [#permalink]

Show Tags

New post 29 Jun 2015, 04:33
Bunuel wrote:
Image

Point a is the center of both a circle and a square. The circle, which is fully shown above, is inscribed in the square and the circle is tangent on all sides with the square, which is only partially shown and has both the x-axis and the y-axis as sides. The origin (0,0) is the bottom-left corner of the square and the line DE is a diagonal of the square. If the x-coordinate of point a is \(x_1\), what is the area of the gray shaded region between the circle and the origin (0,0)?

A) \(0.25(x_1)^2(4 - \pi)\)
B) \((x_1)^2 - (x_1)^2\pi\)
C) \(0.25(2(x_1)^2 - (x_1)^2)\pi)\)
D) \(4(x_1)^2 - (x_1)^2\pi\)
E) \((x_1)^2 - (x_1)^2*0.5\pi\)

Source: Platinum GMAT
Kudos for a correct solution.

Attachment:
00023-1.gif


Platinum GMAT Official Solution:

The general approach to solving this question is that we want to find:
(Area of Square – Area of Circle)/4
=.25(Area of Square – Area of Circle)
Note: We divide by 4 since we are only interested in the bottom left gray region. This will be one fourth of the total region between the circle and the square since the circle is perfectly inscribed into the square due to the circle being tangent with each side of the square.

Since the x-coordinate of point a is x1, point a is x1 units away from the y-axis. This distance from the y-axis to point a is the exact same distance as the length of the radius AF. Consequently, AF = x1 = length of radius. As a result:
Diameter circle = 2(Radius)
Diameter circle = 2(x1)
Note: The diameter is not important for the next step, but it will be important later.

We can now calculate the area of the circle:
Area circle = πr^2
Area circle = π(x1)^2

The area of the square is the length of a side of the square multiplied by itself. Although we are not told directly the length of a side, since the circle is tangent with the square on all sides, we know that the circle will just fit within the square. Consequently, the length of the side of the square is the same as the length of the diameter of the circle:
Diameter circle = Length square
2(x1) = Length of Side of Square

The area of the square:
Area square = side^2
Area square = (2*(x1))^2

Calculate the area of the gray region:
=.25(Area of Square – Area of Circle)
.25[(2x1)^2 - (x1)2π]
.25[4(x1)^2 - (x1)2π]
.25[(x1)^2*4 - (x1)2π]
.25*(x1)^2(4 – π)

Answer: A.
_________________

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8767
Premium Member
Re: Point a is the center of both a circle and a square. The circle, which  [#permalink]

Show Tags

New post 28 Jul 2018, 11:04
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: Point a is the center of both a circle and a square. The circle, which &nbs [#permalink] 28 Jul 2018, 11:04
Display posts from previous: Sort by

Point a is the center of both a circle and a square. The circle, which

  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®.