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

It is currently 18 Sep 2018, 22:21

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

Of the 8 points in a given plane 4 are on circle O -Geometry - PS

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

Hide Tags

Senior Manager
Senior Manager
User avatar
G
Joined: 08 Jun 2013
Posts: 323
Location: India
Schools: INSEAD Jan '19
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Engineering (Other)
GMAT ToolKit User Premium Member
Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

Show Tags

New post 24 Aug 2018, 20:00
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

47% (01:46) correct 53% (01:55) wrong based on 34 sessions

HideShow timer Statistics

Of the 8 points in a given plane 4 are on circle O and remaining 4 are on line L. Number of different quadrilaterals that can be formed by these 8 points are

A) 52

B) 53

C) 54

D) 64

E) 74

_________________

It seems Kudos button not working correctly with all my posts...

Please check if it is working with this post......

is it?....

Anyways...Thanks for trying :cool:

Manager
Manager
avatar
B
Joined: 16 Apr 2018
Posts: 71
Re: Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

Show Tags

New post 24 Aug 2018, 21:02
4C3*4C1 + 4C4 + 4C2*4C2 = 53

Posted from my mobile device
BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3128
Location: India
GPA: 3.12
Premium Member CAT Tests
Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

Show Tags

New post 25 Aug 2018, 00:29
Attachment:
Line_Circle.png


We are given a line and circle each which contain 4 points. The 8 points can be the vertices of a quadrilateral.
A line which has 4 collinear points can have a maximum of 2 points which can be the vertices. There are 3 ways
in which a quadrilateral can be formed

1. All 4 vertices are on the circle - \(C_4^4 = 1\)
2. Three vertices are on the circle and one vertice if on the line - \(C_3^4*C_1^4 = 4*4 = 16\)
3. Two vertices are on the circle and two vertices are on the line - \(C_2^4*C_2^4 = 6*6 = 36\)

Therefore, the total number of quadrilaterals that can be formed by these points are 1+16+36 = 53(Option B)
_________________

You've got what it takes, but it will take everything you've got

DS Forum Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 714
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

Show Tags

New post 25 Aug 2018, 01:30
1
Out of the four points given, A quadrilateral can be formed by selecting \(4\) points from the \(8\) points except when:
i) \(4\) points have been taken from the line
ii) \(3\) points have been taken from the line and one from circle.

Total required cases \(= 8C4- (4C4+4C3*4C1) = 53\)

Answer = B

Harshgmat wrote:
Of the 8 points in a given plane 4 are on circle O and remaining 4 are on line L. Number of different quadrilaterals that can be formed by these 8 points are

A) 52

B) 53

C) 54

D) 64

E) 74

_________________

Win GMAT CLUB Tests - Weekly Quant Quiz Contest
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1973
Premium Member CAT Tests
Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

Show Tags

New post 25 Aug 2018, 09:57
2
pushpitkc wrote:

Therefore, the total number of quadrilaterals that can be formed by these points are 1+16+36 = 52(Option B)

pushpitkc , your post has a typo. Your total says 52. Total should say 53 to match your answer of Option B.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3128
Location: India
GPA: 3.12
Premium Member CAT Tests
Of the 8 points in a given plane 4 are on circle O -Geometry - PS  [#permalink]

Show Tags

New post 25 Aug 2018, 10:07
generis wrote:
pushpitkc wrote:

Therefore, the total number of quadrilaterals that can be formed by these points are 1+16+36 = 52(Option B)

pushpitkc , your post has a typo. Your total says 52. Total should say 53 to match your answer of Option B.


Thanks for notifying, made the necessary change!
Of the 8 points in a given plane 4 are on circle O -Geometry - PS &nbs [#permalink] 25 Aug 2018, 10:07
Display posts from previous: Sort by

Of the 8 points in a given plane 4 are on circle O -Geometry - PS

  post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


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®.