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

It is currently 26 Jul 2014, 07:23

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

At how many points does line L intersect with the parabola

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 29 Nov 2011
Posts: 81
Followers: 1

Kudos [?]: 37 [0], given: 37

At how many points does line L intersect with the parabola [#permalink] New post 01 Feb 2012, 18:16
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

48% (02:04) correct 52% (00:48) wrong based on 82 sessions
At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?

(1) Line L is parallel to x-axis.
(2) Line L passes through the point (0, 16).
[Reveal] Spoiler: OA
2 KUDOS received
Manager
Manager
avatar
Joined: 03 Oct 2009
Posts: 64
Followers: 0

Kudos [?]: 24 [2] , given: 8

Re: Coordinate [#permalink] New post 01 Feb 2012, 20:44
2
This post received
KUDOS
At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?

y = x² - 3x + 6?

Since a (coefficient of x²) is +ve, it's an upward parabola.

y intercept is 6

(1) Line L is parallel to x-axis.
Not sufficient, as we don't know where does it intersects the y axis.

(2) Line L passes through the point (0, 16).
Not sufficient as we don't know the slope, depending on slope line may intersect parabola at zero or multiple points.

(1) + (2)

Sufficient, lines intersects parabola at only two points i.e. where y = 16.

C
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1365
Followers: 10

Kudos [?]: 131 [0], given: 10

GMAT Tests User
Re: Coordinate [#permalink] New post 02 Feb 2012, 00:26
a. means y=0,substituting in the equation we get two values for x.
sufficient.

b y= mx + c meaning y = 0+ 16 (substitution)
clearly no clue about other point and slope.
Not sufficient.

A it is.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Expert Post
Founder
Founder
User avatar
Affiliations: UA-1K, SPG-G, HH-D
Joined: 04 Dec 2002
Posts: 12020
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
WE: Information Technology (Hospitality and Tourism)
Followers: 2161

Kudos [?]: 7635 [0], given: 3626

GMAT ToolKit User Premium Member CAT Tests
Re: At how many points does line L intersect with the parabola [#permalink] New post 02 Feb 2012, 00:31
Expert's post
Smita04 wrote:
At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?
(1) Line L is parallel to x-axis.
(2) Line L passes through the point (0, 16).



What is the source? You did not specify....
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... | Want to know your GMAT Score? Try GMAT Score Estimator
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

Have a blog? Feature it on GMAT Club!

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18741
Followers: 3250

Kudos [?]: 22446 [1] , given: 2619

Re: At how many points does line L intersect with the parabola [#permalink] New post 02 Feb 2012, 08:19
1
This post received
KUDOS
Expert's post
At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?

Generally a parabola and a line can have 0, 1, or 2 intersection points.

Notice than in our case, since the coefficient of x^2 is positive, then we have an upward parabola, which intersects y-axis at (0, 6). Just to illustrate, below is the graph of y = x^2 - 3x + 6:
Attachment:
parabola.gif
parabola.gif [ 3.02 KiB | Viewed 1949 times ]


(1) Line L is parallel to x-axis. All three cases are possible: line L can be below the given parabola (no intersection), line L can go through the vertex (1 intersection) or cross it above the vertex (2 intersections). Not sufficient.

Notice that if it were: line L is parallel to y-axis then we would know that it would cross a parabola at one point, hence in this case the statement would be sufficient.

(2) Line L passes through the point (0, 16). Since (0, 16) is higher than y-intercept of parabola, then line L is "trapped" and must have at least one intersection with parabola (it'll have only one for example if L is y=0). Not sufficient.

(1)+(2) Line L intersect with the parabola at two points. Sufficient.

Answer: C.
_________________

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

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18741
Followers: 3250

Kudos [?]: 22446 [0], given: 2619

Re: At how many points does line L intersect with the parabola [#permalink] New post 27 Jun 2013, 21:29
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

_________________

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

Re: At how many points does line L intersect with the parabola   [#permalink] 27 Jun 2013, 21:29
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic The two perpendicular lines L and R intersect at the point honchos 4 13 Nov 2013, 00:20
5 Experts publish their posts in the topic In xy plane, a certain line L1 has how many intersections shivanigs 6 02 Oct 2012, 23:25
Does line L intersect with the circle centered at the Galiya 8 06 Jul 2011, 11:29
At how many lines does line L intersect parabola represented dana 5 22 Nov 2007, 23:25
1 How many points of intersection does line L and the curve withme 2 18 Jan 2007, 07:35
Display posts from previous: Sort by

At how many points does line L intersect with the parabola

  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®.