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

It is currently 16 Sep 2014, 13:41

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

In the above diagram, the 16 dots are in rows and columns,

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2085
Followers: 513

Kudos [?]: 2110 [0], given: 30

In the above diagram, the 16 dots are in rows and columns, [#permalink] New post 03 Feb 2014, 10:47
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (02:10) correct 67% (01:55) wrong based on 49 sessions
Attachment:
4x4 grid.JPG
4x4 grid.JPG [ 9.78 KiB | Viewed 829 times ]

In the above diagram, the 16 dots are in rows and columns, and are equally spaced in both the horizontal & vertical direction. How many triangles, of absolutely any shape, can be created from three dots in this diagram? Different orientations (reflections, rotations, etc.) and/or positions count as different triangles. (Notice that three points all on the same line cannot form a triangle; in other words, a triangle must have some area.)
(A) 516
(B) 528
(C) 1632
(D) 3316
(E) 3344


Many GMAT math problems, such as this one, cannot be solved by formulas alone. For a discussion of the uses & abuses of formulas on the GMAT Quant section, as well as the complete solution to this problem, see:
http://magoosh.com/gmat/2014/gmat-math- ... -formulas/

Mike :-)
[Reveal] Spoiler: OA

_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
1 KUDOS received
Manager
Manager
avatar
Joined: 09 Oct 2011
Posts: 120
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 760 Q50 V42
GPA: 3
Followers: 2

Kudos [?]: 54 [1] , given: 7

Re: In the above diagram, the 16 dots are in rows and columns, [#permalink] New post 03 Feb 2014, 12:04
1
This post received
KUDOS
Number of ways to select 3 points out of 16 is 16C3 = 560. There is possibility that in some cases out of the 560 cases, the three points lie on the same line and therefore do not form a triangle. This eliminates options B,C and D

There are 4 columns and 4 rows make it a total of 8 linear possible arrangements of the points. Number of ways in which the points can be arranged along each row or column = 8*(4C3) = 8*4 = 32.

We are left with 560-32 =528 ways. Now there is also the possibility that the three points fall on a straight line if placed along the diagonal. Thus the number of ways is definitely less than 528, leaving option A.
_________________

Paras.

If you found my post helpful give KUDOS!!! Everytime you thank me but don't give Kudos, an Angel dies!

My GMAT Debrief:

I am now providing personalized one to one GMAT coaching over Skype at a nominal fee. Hurry up to get an early bird discount! Send me an IM to know more.

1 KUDOS received
Manager
Manager
User avatar
Status: It's Kelley this fall!
Joined: 02 Sep 2013
Posts: 53
Location: India
Concentration: Strategy, Finance
GMAT 1: 750 Q51 V40
GPA: 3.67
WE: Engineering (Other)
Followers: 2

Kudos [?]: 18 [1] , given: 14

GMAT ToolKit User
Re: In the above diagram, the 16 dots are in rows and columns, [#permalink] New post 03 Feb 2014, 23:56
1
This post received
KUDOS
1
This post was
BOOKMARKED
mikemcgarry wrote:
Attachment:
4x4 grid.JPG

In the above diagram, the 16 dots are in rows and columns, and are equally spaced in both the horizontal & vertical direction. How many triangles, of absolutely any shape, can be created from three dots in this diagram? Different orientations (reflections, rotations, etc.) and/or positions count as different triangles. (Notice that three points all on the same line cannot form a triangle; in other words, a triangle must have some area.)
(A) 516
(B) 528
(C) 1632
(D) 3316
(E) 3344


Many GMAT math problems, such as this one, cannot be solved by formulas alone. For a discussion of the uses & abuses of formulas on the GMAT Quant section, as well as the complete solution to this problem, see:
http://magoosh.com/gmat/2014/gmat-math- ... -formulas/

Mike :-)


Number of ways to connect any 3 distinct dots = 16C3 = (16*15*14)/(3*2*1) = 560
Number of ways to connect any 3 distinct dots into a horizontal line (non-triangles) = 4C3*4 = 16
Number of ways to connect any 3 distinct dots into a vertical line (non-triangles) = 4C3 *4 = 16
Number of ways to connect any 3 distinct dots into top-left to bottom-right lines (non-triangles) = 1+4C3+1 = 6
Number of ways to connect any 3 distinct dots into bottom-left to top-right lines (non-triangles) = 1+4C3+1 = 6

Number of ways to connect any 3 distinct dots in the figure into a triangle = 560 - 16 - 16 - 6 - 6 = 516

Choose
[Reveal] Spoiler:
A


Cheers
_________________

Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Intern
Intern
avatar
Joined: 26 Oct 2013
Posts: 24
Followers: 0

Kudos [?]: 4 [0], given: 4

CAT Tests
Re: In the above diagram, the 16 dots are in rows and columns, [#permalink] New post 30 Mar 2014, 08:04
Hello,
Please can someone explain how to calculate the number number of ways to connect any 3 distinct dots into top-left to bottom-right line and into bottom-left to top-right lines.

Why is not 4C3 *2 ?? Why you need to sum 1+ 4C3 +1 ?
3 KUDOS received
Manager
Manager
User avatar
Status: It's Kelley this fall!
Joined: 02 Sep 2013
Posts: 53
Location: India
Concentration: Strategy, Finance
GMAT 1: 750 Q51 V40
GPA: 3.67
WE: Engineering (Other)
Followers: 2

Kudos [?]: 18 [3] , given: 14

GMAT ToolKit User
Re: In the above diagram, the 16 dots are in rows and columns, [#permalink] New post 30 Mar 2014, 09:13
3
This post received
KUDOS
GDR29 wrote:
Hello,
Please can someone explain how to calculate the number number of ways to connect any 3 distinct dots into top-left to bottom-right line and into bottom-left to top-right lines.

Why is not 4C3 *2 ?? Why you need to sum 1+ 4C3 +1 ?


Hope this helps:
Attachment:
4x4 grid.JPG
4x4 grid.JPG [ 44.21 KiB | Viewed 561 times ]


Cheers
_________________

Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Intern
Intern
avatar
Joined: 26 Oct 2013
Posts: 24
Followers: 0

Kudos [?]: 4 [0], given: 4

CAT Tests
Re: In the above diagram, the 16 dots are in rows and columns, [#permalink] New post 30 Mar 2014, 17:46
very nice! Thks a lot !
Re: In the above diagram, the 16 dots are in rows and columns,   [#permalink] 30 Mar 2014, 17:46
    Similar topics Author Replies Last post
Similar
Topics:
1 A table of numbers has n rows and n columns, where n is an o ConnectTheDots 2 03 Apr 2014, 11:39
The above 11 x 11 grid of dots is evenly spaced: each dot is akijuneja 0 03 Jul 2013, 23:46
2 Experts publish their posts in the topic The above 11 x 11 grid of dots is evenly spaced: each dot is mikemcgarry 10 20 May 2013, 10:40
A diagram has exactly two black dots and one green dot for jallenmorris 7 15 May 2008, 14:11
A diagram has exactly 2 black dots and 1 green dot for every cloaked_vessel 10 30 Mar 2005, 18:51
Display posts from previous: Sort by

In the above diagram, the 16 dots are in rows and columns,

  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®.