Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Oct 2014, 00:10

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Circle C and line K lie in the XY plane. If circle C is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 27 Feb 2010
Posts: 106
Location: Denver
Followers: 1

Kudos [?]: 119 [0], given: 14

Circle C and line K lie in the XY plane. If circle C is [#permalink] New post 28 Apr 2010, 06:41
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

55% (01:43) correct 45% (01:12) wrong based on 32 sessions
Circle C and line K lie in the XY plane. If circle C is centered at the orgin and has a radius 1, does line K intersect circle C?

(1) The X-Intercept of line k is greater than 1
(2) The slope of line k is -1/10.
[Reveal] Spoiler: OA
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2794
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 182

Kudos [?]: 986 [0], given: 235

Reviews Badge
Re: Does line K intersect circle C? [#permalink] New post 28 Apr 2010, 06:59
zz0vlb wrote:
Circle C and line K lie in the XY plane. If circle C is centered at the orgin and has a radius 1, does line K intersect circle C?

(1) The X-Intercept of line k is greater than 1
(2) The slope of line k is -1/10.


[Reveal] Spoiler:
E


Let the line is y -mx +c =0

Now if the distance from the center of circle > radius => Line lie outside circle and does intersect with the line.

Distance = \frac{|y1-mx1+c|}{\sqrt{(1+m^2)}}

Distance from (0,0) = \frac{|0*1-m*0+c|}{\sqrt{(1+m^2)}}
= \frac{|c|}{\sqrt{(1+m^2)}}

Since it depends upon both c and m , thus both the statements individually are not sufficient.
So rule out A B and D

Now take 2nd equation m = -1/10

Distance becomes =|c|/\sqrt{{1+\frac{1}{10}^2}}

d = |c|*\sqrt{\frac{100}{101}}

Now c>1, but still we cannot say anything about d as if c > \sqrt{\frac{101}{100}}.
then d>1 else d<1 ( take the case when \sqrt{\frac{101}{100}} > c > 1

thus E
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23359
Followers: 3605

Kudos [?]: 28744 [0], given: 2846

Re: Does line K intersect circle C? [#permalink] New post 28 Apr 2010, 07:38
Expert's post
zz0vlb wrote:
Circle C and line K lie in the XY plane. If circle C is centered at the orgin and has a radius 1, does line K intersect circle C?

(1) The X-Intercept of line k is greater than 1
(2) The slope of line k is -1/10.

[Reveal] Spoiler:
E


No matter what the slope is, it’s possible for line not to cross the circle as the x intercept can be + infinite.

(1) Just says that x intercept is right to the circle. Not sufficient
(2) Just says that slope is -1/10 --> line is just going down. Not sufficient.

(1)+(2) As we don't know exact intercept of line and X-axis we can not determine whether line intersects the circle or not. Not sufficient.

To elaborate more: we can draw infinitely many parallel lines with X-intercept more than 1 and slope -1/10, some will intersect the circle and some not.

Answer: E.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 14 Sep 2009
Posts: 29
Followers: 0

Kudos [?]: 9 [0], given: 22

GMAT PREP DS [#permalink] New post 22 Aug 2010, 17:53
I understand this one a little bit but I'd like some more clarity. As far as statement 2 goes, other than the fact that the slope is negative, what else can I gather from it. Thanks

Circle C and line k lie in the xy-plane. If circle C is centered at the origin and has radius 1, does line k intersect circle C?

(1) The x-intercept of line k is greater than 1
(2) The slope of line k is -1/10
Senior Manager
Senior Manager
avatar
Joined: 14 Jun 2010
Posts: 334
Followers: 2

Kudos [?]: 15 [0], given: 7

Re: Does line K intersect circle C? [#permalink] New post 31 Aug 2010, 22:03
Good explanation by the master!!
Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1726
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 67

Kudos [?]: 328 [0], given: 109

Re: Does line K intersect circle C? [#permalink] New post 01 Sep 2010, 08:41
+1 E

The line may be under the circle and very far. It will never touch the circle.

I think I deserve kudos ;)
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Does line K intersect circle C?   [#permalink] 01 Sep 2010, 08:41
    Similar topics Author Replies Last post
Similar
Topics:
2 Circle C and line k lie in the xy plane. If circle C is nvuppala 6 22 Mar 2011, 16:50
Circle C and Line K lie in the xy-plane. If circle C is kizito2001 3 28 Feb 2008, 16:31
Circle C and line k lie in the xy plane. If Circle C is LM 2 10 Dec 2006, 00:06
Circle C and line K lie in the xy plane. If circle C, Paayal 6 05 Oct 2006, 17:34
Circle C and line k lie in the xy-plane. If circle C is joemama142000 9 18 Dec 2005, 12:26
Display posts from previous: Sort by

Circle C and line K lie in the XY plane. If circle C is

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.