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

It is currently 13 Dec 2019, 13:58

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 and remaining 4 are

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59721
Of the 8 points in a given plane 4 are on circle O and remaining 4 are  [#permalink]

Show Tags

New post 25 Nov 2019, 01:42
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

49% (02:15) correct 51% (01:54) wrong based on 49 sessions

HideShow timer Statistics

VP
VP
User avatar
V
Joined: 19 Oct 2018
Posts: 1174
Location: India
Premium Member CAT Tests
Re: Of the 8 points in a given plane 4 are on circle O and remaining 4 are  [#permalink]

Show Tags

New post 25 Nov 2019, 04:18
2
Total number of possible quadrilaterals
= 4C4+4C3*4C1+4C2*4C2
= 1+16+36
=53

Bunuel 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


Are You Up For the Challenge: 700 Level Questions
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Of the 8 points in a given plane 4 are on circle O and remaining 4 are  [#permalink]

Show Tags

New post 25 Nov 2019, 04:26
together points of circle + line to form quadrilateral
4c3*4c1 + 4c2 * 4c2
=> 16+ 36
=> 52
IMO A
4c3*4c1 + 4c2 * 4c2+4c4
using all the points possible quadrilateral = 16+ 36+1 ; 53
IMO B


Bunuel 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


Are You Up For the Challenge: 700 Level Questions
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 971
Location: United States
Re: Of the 8 points in a given plane 4 are on circle O and remaining 4 are  [#permalink]

Show Tags

New post 26 Nov 2019, 08:57
2
Bunuel 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


cases circle + line:
4C2*4C2=36
4C3*4C1=16

cases circle only:
4C4=1

total: 36+16+1=53

Ans (B)
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8695
Location: United States (CA)
Re: Of the 8 points in a given plane 4 are on circle O and remaining 4 are  [#permalink]

Show Tags

New post 02 Dec 2019, 19:12
1
2
Bunuel 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


Are You Up For the Challenge: 700 Level Questions


The four points on circle O are not collinear; however, the four points on line L are. The three methods to form a quadrilateral, using four of the eight points, are:

1) All four points are from circle O,

2) Three points are from circle O, and one point is from line L, and

3) Two points are from circle O, and two points are from line L.

Let’s now determine the number of ways for each method.

1) All four points are from circle O

The number of ways using this method is 4C4 = 1.

2) Three points from circle O and one point from line L

The number of ways using this method is 4C3 x 4C1 = 4 x 4 = 16.

3) Two points from circle O and two points from line L

The number of ways using this method is 4C2 x 4C2 = 6 x 6 = 36.

Therefore, the total number of quadrilaterals that can be formed is 1 + 16 + 36 = 53.

Alternate Solution:

From a total of 8 points, 4 points can be chosen in 8C4 = 8!/(4!*4!) = 70 ways.

Among these 70 choices, the following will not form a quadrilateral:

1) All the four points are from line L. There’s only one such choice.

2) Three points are from line L and one point from circle O: The three points can be chosen from the line in 4C3 = 4 ways. The one point can be chosen from the circle in 4C1 = 4 ways. Thus, there are 4 x 4 = 16 such choices.

We see that 16 + 1 = 17 of the 70 choices of four points do not form a quadrilateral and 70 - 17 = 53 choices do.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: Of the 8 points in a given plane 4 are on circle O and remaining 4 are   [#permalink] 02 Dec 2019, 19:12
Display posts from previous: Sort by

Of the 8 points in a given plane 4 are on circle O and remaining 4 are

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne