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

It is currently 22 Sep 2018, 23:40

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

Given a circle that is inscribed in a rectangle so that the circle tou

  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: 49303
Given a circle that is inscribed in a rectangle so that the circle tou  [#permalink]

Show Tags

New post 06 Sep 2018, 01:17
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (00:20) correct 27% (00:40) wrong based on 19 sessions

HideShow timer Statistics

Image
Given a circle that is inscribed in a rectangle so that the circle touches all four sides of the rectangle as shown in the figure, what is the area of the shaded region?

(1) The rectangle shown is a square.
(2) The area of the shown circle is 10π.


Attachment:
image011.gif
image011.gif [ 776 Bytes | Viewed 175 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
G
Joined: 18 Jul 2018
Posts: 192
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member CAT Tests
Re: Given a circle that is inscribed in a rectangle so that the circle tou  [#permalink]

Show Tags

New post 06 Sep 2018, 02:36
From statement 1:

No info about the side of a square or the radius of the circle.
Hence insufficient.

From statement 2:
Area = 10Pi
Pi*\(r^2\) = 10Pi
r = \(\sqrt{10}\)

Diameter = 2r = 2\(\sqrt{10}\) = Side of the square.

Area of the shaded region = area of the square - area of the circle.

Area of the shaded region = 4*10-10Pi = 40-10Pi.

Hence 2 is sufficient.

B is the answer.
Manager
Manager
User avatar
S
Joined: 11 Aug 2016
Posts: 215
Reviews Badge CAT Tests
Re: Given a circle that is inscribed in a rectangle so that the circle tou  [#permalink]

Show Tags

New post 06 Sep 2018, 03:05
Quote:
Given a circle that is inscribed in a rectangle so that the circle touches all four sides of the rectangle as shown in the figure, what is the area of the shaded region?

(1) The rectangle shown is a square.
(2) The area of the shown circle is 10π.



Statement 1: The rectangle shown is a square.
No new information.
If a circle touches all four sides of a rectangle, the rectangle has to be a square.
Insufficient.

Statement 2: The area of the shown circle is 10π.
We already know that the circle touches all four sides of the rectangle. Hence the rectangle is a square.
That means all the sides are equal.
In addition, this statement gives us the area of circle.
There is no need of calculations.
From Area, we can calculate the radius of the circle, r.
Also, from the figure we can see that the side of the square = dia of circle= 2xr
hence we can calculate the area of square.
Subtracting the area of Square from the area of circle, we get the area of shaded region.
Hence, Sufficient

Answer: B

Please Note that questions like above, are intentionally put up to make the test taker waste time.
There's no need of any calculation. We just have to check out the basics of Data sufficiency, ie if the information given is sufficient.

_________________

~R.
If my post was of any help to you, You can thank me in the form of Kudos!!

GMAT Club Bot
Re: Given a circle that is inscribed in a rectangle so that the circle tou &nbs [#permalink] 06 Sep 2018, 03:05
Display posts from previous: Sort by

Given a circle that is inscribed in a rectangle so that the circle tou

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

Events & Promotions

PREV
NEXT


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®.