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

It is currently 18 Dec 2018, 09:21

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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Happy Christmas 20% Sale! Math Revolution All-In-One Products!

     December 20, 2018

     December 20, 2018

     10:00 PM PST

     11:00 PM PST

    This is the most inexpensive and attractive price in the market. Get the course now!
  • Key Strategies to Master GMAT SC

     December 22, 2018

     December 22, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

The above picture depicts a circle perfectly inscribed in a square. Is

  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: 51280
The above picture depicts a circle perfectly inscribed in a square. Is  [#permalink]

Show Tags

New post 25 Aug 2015, 23:46
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (02:12) correct 30% (02:01) wrong based on 122 sessions

HideShow timer Statistics

Image
The above picture depicts a circle perfectly inscribed in a square. Is the shaded region > 4?

(1) The area of the large rectangle equals 64.
(2) The perimeter of the shaded region equals 8 + 2π.

Kudos for a correct solution.

Attachment:
circle-in-square-red2.GIF
circle-in-square-red2.GIF [ 2.24 KiB | Viewed 1558 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

Manager
Manager
User avatar
Joined: 14 Mar 2014
Posts: 146
GMAT 1: 710 Q50 V34
The above picture depicts a circle perfectly inscribed in a square. Is  [#permalink]

Show Tags

New post 26 Aug 2015, 08:59
IMO: D

Consider the following fig:
Attachment:
Capture.JPG
Capture.JPG [ 15.19 KiB | Viewed 1388 times ]



Question Stem: Area of the shaded region = \(\frac{[Area of the square - Area of the cirlce]}{4}\)
Area of square = 2r*2r = \(4r^2\)
Area of Circle = \(πr^2\)
Area of the shaded region = \(\frac{[4r^2 - πr^2]}{4}\)

IS \(\frac{r^2[4 - π]}{4}\) > 4 ?

IS \(r^2[4 - π]\) > 16 ? -- (i)

St 1: The area of the large rectangle equals 64.

I think the question is flawed. PSTU is a rectangle and PQRS is also a rectangle(Every square is a rectangle). The use of word large is ambiguous. It can either represent PSTU or PQRS. If largest is used instead then PQRS can be considered which would be sufficient alone as well.

Area of PSTU = 64
Where PS = 2r & SU = r
Thus, 2r*r = 64
\(r^2\)= 32 ---(ii)

Sub in Eq - (i)
\(32[4 - π]\) > 16 ? YES
Hence Suff

St 2: The perimeter of the shaded region equals 8 + 2π

Perimeter of the shaded region = Length of the arc TV + Side TQ + Side QV

Length of the arc = \(\frac{θ}{360} * 2πr\)
= \(\frac{90}{360} * 2πr\)
= \(\frac{πr}{2}\)

Thus,

\(8 + 2π = \frac{πr}{2} + r + r\)
r = 4
Sub in eq--(i)
\(r^2[4 - π]\) > 16 ?
\(16[4 - π]\) > 16 ? YES
Hence Suff
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯ :-)

Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 294
Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: The above picture depicts a circle perfectly inscribed in a square. Is  [#permalink]

Show Tags

New post 26 Aug 2015, 18:11
2
shaded region > 4?
If we can determine the radius, we can determine the side of the square and the rectangle, allowing us to find the area of the square, rectangle and circle. What is the radius?

(1) The area of the large rectangle equals 64.
r*2r=64
Sufficient

(2) The perimeter of the shaded region equals 8 + 2π.
8 + 2π = (2πr)/4 + 2r
Sufficient

Answer: D
SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 1919
Reviews Badge CAT Tests
Re: The above picture depicts a circle perfectly inscribed in a square. Is  [#permalink]

Show Tags

New post 27 Aug 2015, 03:33
Hi Bunuel:
Can you please advise? How come in the same question we get different answers.
In statement 1: r=4\sqrt{2}
In Statement 2: r =4
Clearly, the question is flawed or do I miss something?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: The above picture depicts a circle perfectly inscribed in a square. Is  [#permalink]

Show Tags

New post 30 Aug 2015, 08:33
Bunuel wrote:
Image
The above picture depicts a circle perfectly inscribed in a square. Is the shaded region > 4?

(1) The area of the large rectangle equals 64.
(2) The perimeter of the shaded region equals 8 + 2π.

Kudos for a correct solution.

Attachment:
circle-in-square-red2.GIF


GROCKIT OFFICIAL SOLUTION:

Statement 1: By knowing the area of the large square we also know the lengths of its sides. (Note that 64 is a perfect square, which should be a clue.) If the side is 8, then so is the diameter, which means the radius equals 4. In the image, we can see that the “larger figure” is the top-right square bordered by two radii and the outer border. How do we know that it’s a square? Two pieces of information: All sides are equal to 4, and the radius meets the large square at a right angle because it is a tangent. In this instance, the area of the smaller square equals 16. Since the interior angle is 90-degrees (360/4), the area of the sector of the circle can be represented by A = πr²/4. So that A = 16π/4 = 4π.

A(shaded) = A(small square) – A(sector) = 16 – 4π < 4 because 4π > 12. Sufficient.

Statement 2: The first thing that should jump out is the combination of a π-term and non- π-term. We can reasonably assume that 8 represents the two straight sides of the perimeter and the 2π the arc-length of the quarter circle, which is known because of the internal right angle. If 2π = C/4, then C = 8π. If C = 8π, then r = 4. From here, we return to the same reasoning as above:

A(shaded) = A(small square) – A(sector) = 16 – 4π < 4 because 4π > 12. Sufficient.

Each statement is sufficient, so the answer is choice D.
_________________

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: 9206
Premium Member
Re: The above picture depicts a circle perfectly inscribed in a square. Is  [#permalink]

Show Tags

New post 12 Jul 2018, 11:01
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: The above picture depicts a circle perfectly inscribed in a square. Is &nbs [#permalink] 12 Jul 2018, 11:01
Display posts from previous: Sort by

The above picture depicts a circle perfectly inscribed in a square. Is

  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®.