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

It is currently 22 Apr 2019, 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

Two spherical balls lie on the ground touching. If one of

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

Hide Tags

 
Manager
Manager
avatar
Status: GMAT in 4 weeks
Joined: 28 Mar 2010
Posts: 157
GPA: 3.89
Two spherical balls lie on the ground touching. If one of  [#permalink]

Show Tags

New post 19 May 2011, 07:31
3
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (03:50) correct 46% (02:30) wrong based on 42 sessions

HideShow timer Statistics

Two spherical balls lie on the ground touching. If one of the balls has a radius of 8 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball?

(A) 18 cm
(B) 40/3 cm
(C) 25/2 cm
(D) 13 cm
(E) none of the these

_________________
If you liked my post, please consider a Kudos for me. Thanks!
Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 372
Schools: Simon '16 (M$)
Re: Two spherical balls lie on the ground touching  [#permalink]

Show Tags

New post 19 May 2011, 10:01
2
See the attached image. smaller circle has radius 8. Consider two triangle. One with hypotenuse 8 and another with hypotenuse 8+x

In smaller triangle, sides are \(8,2,2\sqrt{15}\)
sin@ = 2/8=1/4

In larger triangle, sides are \(8+x, 2\sqrt{15}+10, x-8\)
sin@= x-8/x+8
1/4=x-8/x+8
x=40/3.
Attachments

img.JPG
img.JPG [ 10.47 KiB | Viewed 5171 times ]


_________________
My dad once said to me: Son, nothing succeeds like success.
Director
Director
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 976
Re: Two spherical balls lie on the ground touching  [#permalink]

Show Tags

New post 21 May 2011, 01:08
similar triangle properties..

2/r+8 = 8/r-8

giving r = 40/3.
Manager
Manager
avatar
Joined: 10 Jan 2010
Posts: 96
GPA: 4
WE: Programming (Computer Software)
Re: Two spherical balls lie on the ground touching  [#permalink]

Show Tags

New post 12 Jun 2011, 16:35
How do we know the line joining the two centre's passes through the point of intersection of the two circles?.

Can somebody please clarify this?.
_________________
-If you like my post, consider giving KUDOS
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9129
Location: Pune, India
Re: Two spherical balls lie on the ground touching  [#permalink]

Show Tags

New post 12 Jun 2011, 19:34
1
maheshsrini wrote:
How do we know the line joining the two centre's passes through the point of intersection of the two circles?.

Can somebody please clarify this?.


For the moment, just think of the two circles touching each other at point, say P, as shown in the diagram in the post by jamifahad.

Now, say, you draw a tangent at P, the point of intersection. This will be a common tangent to both the circles at the point P. Join the center of each circle with P. We know that the line joining the center to the point of tangency will be perpendicular to the tangent.
Hence they will form an angle of 180 degrees and will therefore be straight.
_________________
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 >
Current Student
avatar
Joined: 26 May 2005
Posts: 498
Re: Two spherical balls lie on the ground touching  [#permalink]

Show Tags

New post 12 Jun 2011, 22:22
hussi9 wrote:
Two spherical balls lie on the ground touching. If one of the balls has a radius of 8 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball?

(1) 18 cm (2) 40/3 cm (3) 25/2 cm (4) 13 cm (5) none of the these


I think using similar triangle property is the best
From the diagram below , we know
triangle CDA is similar triangle BEA
therefore
BE/EA= CD/DA..... (DA is the radius we are looking for)
2/8 = (r-8)/(r+8)
solve to get r = 40/3
Attachments

circle.jpg
circle.jpg [ 14.38 KiB | Viewed 4784 times ]

Manager
Manager
avatar
Joined: 10 Jan 2010
Posts: 96
GPA: 4
WE: Programming (Computer Software)
Re: Two spherical balls lie on the ground touching  [#permalink]

Show Tags

New post 13 Jun 2011, 08:01
yeah, got it. Thanks Karishma.
_________________
-If you like my post, consider giving KUDOS
Intern
Intern
avatar
B
Joined: 09 Jan 2017
Posts: 2
Re: Two spherical balls lie on the ground touching. If one of  [#permalink]

Show Tags

New post 08 Jul 2017, 05:16
I have a query.
In the ques it it stated that "the point of contact is 10 cm above the ground". But in the images of solutions proposed, the value 10 is suggested as distance between point of contacts of circles with the ground.
Can someone clarify what I am missing in comprehending the problem?
GMAT Club Bot
Re: Two spherical balls lie on the ground touching. If one of   [#permalink] 08 Jul 2017, 05:16
Display posts from previous: Sort by

Two spherical balls lie on the ground touching. If one of

  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®.