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

It is currently 21 Jul 2018, 08:48

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

How many different-sized circles with positive integer radii have area

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47166
How many different-sized circles with positive integer radii have area  [#permalink]

Show Tags

New post 28 Nov 2017, 21:02
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

68% (00:45) correct 32% (00:55) wrong based on 22 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
G
Joined: 17 Oct 2016
Posts: 325
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
GMAT ToolKit User Premium Member CAT Tests
Re: How many different-sized circles with positive integer radii have area  [#permalink]

Show Tags

New post 28 Nov 2017, 21:29
B

For radius=6 the area is 113.09>100. Hence only upto 5


Sent from my iPhone using GMAT Club Forum
_________________

Help with kudos if u found the post useful. Thanks

SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1833
Premium Member CAT Tests
How many different-sized circles with positive integer radii have area  [#permalink]

Show Tags

New post 29 Nov 2017, 16:13
1
Bunuel wrote:
How many different-sized circles with positive integer radii have areas less than 100?

(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen

I can see potential trouble with area = 100.

Area of circle is \(πr^2\).

So it must be \(r^2 * 3.14 < 100\), where r is an integer.

Radii 1, 2, 3, 4, and 5 (25 * 3.14 = approx 78) work.

Radius 6 does not: 36 * 3 = 108, so with 3.14 it would be higher.

Five values satisfy the conditions.

Answer B
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2973
Location: United States (CA)
Re: How many different-sized circles with positive integer radii have area  [#permalink]

Show Tags

New post 01 Dec 2017, 07:54
Bunuel wrote:
How many different-sized circles with positive integer radii have areas less than 100?

(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen


If r = 1, then the area of the circle is π(1)^2 = π.

If r = 2, then the area is π(2)^2 = 4π.

If r = 3, then the area is π(3)^2 = 9π.

If r = 4, then the area is π(4)^2 = 16π.

If r = 5, then the area is π(5)^2 = 25π.

Since π < 4, the area of any of the circles above will be less than 100. However, if r = 6, then the area of the circle will be π(6)^2 = 36π. However, since π > 3, 36π will be greater than 100. Thus, there are five different-sized circles with positive integer radii with area less than 100.

Answer: B .
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: How many different-sized circles with positive integer radii have area &nbs [#permalink] 01 Dec 2017, 07:54
Display posts from previous: Sort by

How many different-sized circles with positive integer radii have area

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

Events & Promotions

PREV
NEXT


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®.