Find all School-related info fast with the new School-Specific MBA Forum
Learn more about the recent changes... close

It is currently 21 May 2013, 09:56
Customize  |  Hide

Search
Register
New posts
Unanswered

M17 #12

  Question banks Downloads My Bookmarks Reviews  
  Oldest Best Reply
Search for:
 
Print view
First unread post
Author Message
Manager
Manager
Joined: 25 Jul 2010
Posts: 147
Followers: 1

Kudos [?]: 13 [0], given: 29

GMAT Tests User
M17 #12 [#permalink] New post 09 Oct 2010, 01:53
00:00

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Is line Y = KX + B tangent to circle X^2 + Y^2 = 1 ?

1. K + B = 1
2. K^2 + B^2 = 1

A) Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
B) Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D) EACH statement ALONE is sufficient
E) Statements (1) and (2) TOGETHER are NOT sufficient
1 KUDOS received
Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 815
Location: London
Followers: 56

Kudos [?]: 301 [1] , given: 25

GMAT ToolKit User GMAT Tests User Reviews Badge
Re: M17 #12 [#permalink] New post 09 Oct 2010, 02:05
1
This post received
KUDOS
Orange08 wrote:
Is line Y = KX + B tangent to circle X^2 + Y^2 = 1 ?

1. K + B = 1
2. K^2 + B^2 = 1

A) Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
B) Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D) EACH statement ALONE is sufficient
E) Statements (1) and (2) TOGETHER are NOT sufficient


Lets solve the equations simultaneously. If a line is a tangent to the circle the equations will have exactly one solution which is the point of intersection.

y=kx+b
x^2+y^2=1
x^2+(kx+b)^2=1
(1+k^2)x^2+2kbx+b^2-1=0

For a quadratic equation to have a single solution, the discriminant (b^2-4ac) must be 0. Therefore :

(2kb)^2 - 4(1+k^2)(b^2-1)=0
4k^2b^2 - 4(b^2-1+k^2b^2-k^2)=0
-4b^2+4+4k^2=0
b^2-k^2=1

(1)k+b=1. Insufficient to show b^2-k^2=1
(2)b^2+k^2=1, Insufficient to show b^2-k^2=1
(1+2) Both together are also insufficient

Answer is (e)

You can also refer to coordinate-geometry-69516.html for an example based approach
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

Find out what's new at GMAT Club - latest features and updates

Manager
Manager
Joined: 25 Jul 2010
Posts: 147
Followers: 1

Kudos [?]: 13 [0], given: 29

GMAT Tests User
Re: M17 #12 [#permalink] New post 09 Oct 2010, 02:18
super. Many thanks.
GMAT Club team member
User avatar
Joined: 02 Sep 2009
Posts: 11534
Followers: 1795

Kudos [?]: 9557 [0], given: 826

GMAT Tests User CAT Tests
Top Member of the Month
Re: M17 #12 [#permalink] New post 09 Oct 2010, 02:29
Orange08 wrote:
Is line Y = KX + B tangent to circle X^2 + Y^2 = 1 ?

1. K + B = 1
2. K^2 + B^2 = 1


The circle represented by the equation x^2+y^2 = 1 is centered at the origin and has the radius of r=\sqrt{1}=1 (for more on this check Coordinate Geometry chapter of math book: math-coordinate-geometry-87652.html ).

(1) K + B = 1 --> if k=0 and b=1 then the equation of the line becomes y=1 and this line is tangent to the circle but if k=1 and b=0 then th equation of the line becomes y=x and this line is NOT tangent to the circle. Not sufficient.

(2) K^2 + B^2 = 1. The same example is valid for this statement too. Not sufficient.

(1)+(2) Again the same example satisfies both statement: if k=0 and b=1 then the equation of the line becomes y=1 and this line is tangent to the circle but if k=1 and b=0 then th equation of the line becomes y=x and this line is NOT tangent to the circle. Not sufficient.

Answer: E.
Attachment:
graph.php.png
graph.php.png [ 15.97 KiB | Viewed 213 times ]

_________________

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

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. NEW!!!

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. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Re: M17 #12   [#permalink] 09 Oct 2010, 02:29
    Similar topics Author Replies Last post
Similar
Topics:
 Popular new posts 1 EXPERTS_POSTS_IN_THIS_TOPIC M17-16 sondenso 16 26 May 2008, 03:55
Popular new posts 6 EXPERTS_POSTS_IN_THIS_TOPIC M17Q5 ventivish 21 30 Oct 2008, 18:05
Popular new posts 11 EXPERTS_POSTS_IN_THIS_TOPIC m17 #8 sharmar 18 05 Dec 2008, 19:08
New posts EXPERTS_POSTS_IN_THIS_TOPIC m 17 #27 pmal04 9 27 Jun 2009, 13:05
New posts M17 Q12 abhi758 1 02 Jun 2010, 01:46
Display posts from previous: Sort by

M17 #12

  Question banks Downloads My Bookmarks Reviews  
Print view
First unread post

Moderator: Bunuel

Search for:


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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com