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

It is currently 18 Apr 2019, 11:37

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

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

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

Hide Tags

 
Manager
Manager
avatar
Joined: 23 Sep 2009
Posts: 109
Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post Updated on: 02 Apr 2019, 03:36
2
28
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

56% (01:55) correct 44% (01:52) wrong based on 388 sessions

HideShow timer Statistics

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

_________________
Thanks,
VP

Originally posted by vigneshpandi on 21 Sep 2010, 21:28.
Last edited by Bunuel on 02 Apr 2019, 03:36, edited 2 times in total.
Edited the question
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54369
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 21 Sep 2010, 21:56
10
5
Circle C and line K lie in the XY plane. If circle C is centered at the origin and has a radius 1, does line K intersect circle C?

The best way to solve this question would be to visualize/draw it.

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

(1) The X-Intercept of line k is greater than 1 --> Just says that X-intercept is to the right of the circle. Not sufficient
(2) The slope of line k is -1/10 --> Just says that slope is negative -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 (for example line with X-intercept 1.1) and some not (for example line with X-intercept 1,000,000). Check the image below for two possible scenarios: blue line (with the slope of -1/10 and the x-Intercept greater than 1) intersects the circle while the red line (also with the slope of -1/10 and the x-Intercept greater than 1) does not.

Image

Answer: E.

For more on this issue check Coordinate Geometry Chapter of Math Book: http://gmatclub.com/forum/math-coordina ... 87652.html

Hope it helps.

Attachment:
graph.png
graph.png [ 15.11 KiB | Viewed 18424 times ]

_________________
General Discussion
Manager
Manager
avatar
Joined: 23 Sep 2009
Posts: 109
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 22 Sep 2010, 16:40
Thank you for the explanation....And the Math book is really helpfull.
_________________
Thanks,
VP
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9119
Location: Pune, India
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 09 Nov 2010, 05:56
anilnandyala wrote:
circle c & line k lie in xy-plane. if circle c is centered at the origin & has a radius 1 . does line k intersect circle c?

1 the x intercept of line k>1
2 the slope of line k= -(1/10)


Look at the diagrams.

Statement 1: If x intercept > 1, the line can be any of the following (and can be drawn in many more ways)
Attachment:
Ques.jpg
Ques.jpg [ 16.54 KiB | Viewed 17216 times ]


Statement 2: If slope = -1/10, the line can be drawn in any of the following ways. (and many more)
Attachment:
Ques1.jpg
Ques1.jpg [ 14.73 KiB | Viewed 17213 times ]


Using both together: Look at the diagrams above. Both have x intercepts greater than 1 and slope = -1/10. In one case, it will intersect the circle, in the other case, it will not. SO both statements together are not sufficient. Answer (E).
_________________
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 >
SVP
SVP
User avatar
G
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1541
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 06 Nov 2011, 22:17
Using statement 1: If the X-intercept of line K is greater than 1, it may or not intersect circle C. For example, if the line is x=3 then it does not intersect the circle C, but if the line is y = -x/4 + 1/2 then it has x-intercept = 2 (>1) and does intersect the circle C. Therefore statement (1) is insufficient.

Using statement 2: If the slope of the line is -1/10, then it may or may not intersect the circle C. For example, y= -x/10 + 2 does not intersect the circle, but y = -x/10 + 0.5 does intersect the circle, though both have a slope of -1/10. Therefore statement 2 is insufficient to answer the question.

Combining statements 1 and 2, the statements together are still insufficient to answer the question. For example, y = -x/10 + 0.5 has an x-intercept greater than 1 and a slope of -1/10, but it does intersect the circle C. However, y = -x/10 + 2 also has an x-intercept greater than 1 and a slope of -1/10, but it does not intersect the circle C.

The answer is (E).
_________________
GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9119
Location: Pune, India
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 07 Nov 2011, 04:08
2
SwapnilRanadive wrote:
Circle C and line K lie in XY plane. If circle C is centered at the origin and has radius 1, does line K intersect circle C?
1) X intercept of line K is greater than 1
2) The slope of like K is -1/10

Pls discuss answer.


Draw some diagrams to figure it out. Even using both statements, you get two cases - one in which K intersects C and another in which it doesn't.

Attachment:
Ques4.jpg
Ques4.jpg [ 9.68 KiB | Viewed 17215 times ]

_________________
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 >
Director
Director
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 976
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 08 Nov 2011, 00:58
a. y=mx+c so for x= -c/m where m can be 1 or -1. c can be 0.1 or 100.

hence a is POE thus D is POE too.

similarly for b too 'c' can have any such values as a.

thus POE.

a+b

y= -0.1x +c meaning x= c/0.1 > 1 thus c > 0.1
hence y intercept can be 0.1 with a slope of -0.1
or 100 with the same slope. not sufficient.

E it is.
Manager
Manager
avatar
Joined: 12 Oct 2011
Posts: 179
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 17 Dec 2011, 00:10
E it is. The diagramming method as shown by Karishma worked best for me.

Statement 1 is insufficient as it gives only x intercept. A line with an x-intercept > 1 may or may not pass through the circle given. INSUFFICIENT.

Statement 2 gives a negative slope. The line is decreasing as it goes from left to right but it does not give an indication whether the line intersects the circle or not. INSUFFICIENT.

Even taken together, two lines can be drawn both with x-intercept more than one and with given negative slope. One of the lines may intersect the circle and the other may not. INSUFFICIENT.

Thus the answer is E.
SVP
SVP
User avatar
G
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1541
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 16 Feb 2012, 21:18
We can see that the circle is centered at origin with radius 1 and has the equation x^2 + y^2 = 1

Using statement (1): If the x-intercept of line k is greater than 1, it may or may not intersect the circle. The line can have any slope and any x-intercept and not all of such lines will intersect with the circle. Insufficient.

Using statement (2): Just knowing the slope without any point that the line passes through is insufficient as with a particular slope infinite lines can be drawn that do and do not intercept the circle. Insufficient.

Combining statement (1) and (2), we get a definite equation of one unique line as we know the x-intercept and the slope. Therefore we can conclude that this line will either intersect the circle or will not. Sufficient.

(C) is the answer.
_________________
GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9119
Location: Pune, India
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 16 Oct 2016, 10:27
Responding to a pm:

Quote:
I have solved the question correctly but in a totally different way. kindly let me know if my process is alright.
statement 1: x=-(c/m)>1
hence slope is less than 0 so the line may or may not touch the circle.

Statement 2: slope is negative hence the line is downward moving. thus it can or cannot touch the circle.

Combining the statement no new info found hence E.

Plus can you please give me some insights on the concept of intercepts?


How do you figure that slope is negative from statement 1?

Slope = - y intercept/x intercept
So you get
m = -c/x (correct)
x = -c/m > 1

Here is my problem: why do you say that m must be negative? c could be negative instead.

Though using both statements, we know that x intercept is greater than 1 and the slope is negative.
_________________
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 >
Director
Director
User avatar
G
Joined: 26 Oct 2016
Posts: 634
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 06 Feb 2017, 20:42
(1) The x-intercept of line K is greater than 1 implies that the x-intercept of line K is towards the right of circle C but this does not imply if line K intersects circle C; NOT sufficient.

(2) The slope of line K is -1/10 implies line K goes down left to right, but again this does not imply if line K intersects circle C; NOT sufficient.

Combining (1) and (2), we do not know the exact intercept of line K, and we cannot find if line K intersects circle C or not; NOT sufficient.

The correct answer is E.
_________________
Thanks & Regards,
Anaira Mitch
Director
Director
avatar
G
Joined: 29 Jun 2017
Posts: 633
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 01 Mar 2018, 07:04
vigneshpandi 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



we do not to draw many things.

if k is perpendicular to x axis , k must be paralel to y axis. k have negative slope this mean k can not parallel to y, so if x intercept is greater than 1, k can cut the circle.

if we move k to the right, k can not cut circle
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 10541
Re: Circle C and line K lie in the XY plane. If circle C is centered at th  [#permalink]

Show Tags

New post 02 Apr 2019, 02:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: Circle C and line K lie in the XY plane. If circle C is centered at th   [#permalink] 02 Apr 2019, 02:18
Display posts from previous: Sort by

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

  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®.