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

It is currently 16 Dec 2018, 16:28

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.
  • Free GMAT Prep Hour

     December 16, 2018

     December 16, 2018

     03:00 PM EST

     04:00 PM EST

    Strategies and techniques for approaching featured GMAT topics

The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior

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

Hide Tags

Manager
Manager
User avatar
Joined: 19 Aug 2010
Posts: 68
The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior  [#permalink]

Show Tags

New post 19 Feb 2011, 10:35
3
20
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (02:33) correct 28% (02:36) wrong based on 242 sessions

HideShow timer Statistics

The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior points respectively on them. How many triangles can be formed using these points as vertices.

A. 200
B. 205
C. 400
D. 410
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51229
Re: How many triangles can be formed  [#permalink]

Show Tags

New post 19 Feb 2011, 10:57
9
7
medanova wrote:
The sides BC,CA,AB of triangle ABC have 3,4,5 interior points respectively on them. How many triangles can be formed using these points as vertices.
a.200
b.205
c.400
d.410


Total points: 3+4+5=12;

Any 3 points out of 12 but those which are collinear will form a triangle, so \(C^3_{12}-(C^3_{3}+C^3_{4}+C^3_{5})=220-(1+4+10)=205\).

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Manager
Manager
User avatar
Joined: 19 Aug 2010
Posts: 68
Re: How many triangles can be formed  [#permalink]

Show Tags

New post 19 Feb 2011, 11:01
Thank you ,

I initially included also the points A B C in the calculation but now I read the question again and found my mistake.
Retired Thread Master
User avatar
Joined: 27 Jan 2010
Posts: 140
Concentration: Strategy, Other
WE: Business Development (Consulting)
Re: How many triangles can be formed  [#permalink]

Show Tags

New post 25 Feb 2011, 09:55
3
1
medanova wrote:
The sides BC,CA,AB of triangle ABC have 3,4,5 interior points respectively on them. How many triangles can be formed using these points as vertices.
a.200
b.205
c.400
d.410


Using 1 point from each side of the triangle -
3C1 * 4C1 * 5C1 = 3 * 4 * 5 = 60

Using 1 point on 1 side and 2 points on the other side -
(3C1 * 4C2) + (3C1 * 5C2) + (4C1 * 3C2) + (4C1 * 5C2) + (5C1 * 4C2) + (5C1 * 3C2) = 145

Adding these we get = 60 + 145 = 205.

I was a little bit confused at first - I was not sure if we could use 2 of the interior points and 1 of the vertices of the existing triangle ABC (as the 3rd vertice) to form a new triangle. I needed to look at the question this way - How many triangles can be formed using only these points as vertices.
Manager
Manager
avatar
Joined: 26 Sep 2010
Posts: 129
Nationality: Indian
Concentration: Entrepreneurship, General Management
GMAT ToolKit User Reviews Badge
Re: How many triangles can be formed  [#permalink]

Show Tags

New post 25 Feb 2011, 22:20
Thanks for the question and great explanations.
_________________

You have to have a darkness...for the dawn to come.

Manager
Manager
User avatar
Joined: 19 Aug 2010
Posts: 68
Re: How many triangles can be formed  [#permalink]

Show Tags

New post 26 Feb 2011, 07:34
Thanks also from me.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51229
Re: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior  [#permalink]

Show Tags

New post 10 Sep 2013, 05:25
Manager
Manager
User avatar
Joined: 20 Jul 2012
Posts: 128
Location: India
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior  [#permalink]

Show Tags

New post 10 Sep 2013, 09:57
medanova wrote:
The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior points respectively on them. How many triangles can be formed using these points as vertices.

A. 200
B. 205
C. 400
D. 410

[1*3*4]*5=60- when all the three points are on different sides..
[1*3+1*6]*5 +[1*10+1*3]*4+[1*10+1*6]*3=45+52+48-when two points on one side
total=60+45+52+48=205
Current Student
User avatar
Joined: 17 Oct 2015
Posts: 22
Concentration: Technology, Leadership
Re: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior  [#permalink]

Show Tags

New post 09 Jan 2016, 05:35
Bunuel, is there a easier way to do the math, instead of multiplying 12 x 11 x 10 x 9 x 8 x 7.....?

As far I understood your solution, I would need to do that at the C 3 12 combination.

Regards and have a great year!

Bunuel wrote:
Bumping for review and further discussion.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7108
Re: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior  [#permalink]

Show Tags

New post 09 Jan 2016, 05:51
4
mestrec wrote:
Bunuel, is there a easier way to do the math, instead of multiplying 12 x 11 x 10 x 9 x 8 x 7.....?

As far I understood your solution, I would need to do that at the C 3 12 combination.

Regards and have a great year!

Bunuel wrote:
Bumping for review and further discussion.


Hi,
Iwillhelp you out on that ..
the Q basically says there are three lines with 3,4,5 points respectively..
lets find ways triangle can be formed..
triangle requires three points,..
1) 2 points from line containing 3 points and one from remaining 4+5 points=3C2*(4+5)=27..
2) 2 points from line containing 4 points and one from remaining 3+5 points=4C2*(3+5)=48..
3) 2 points from line containing 5 points and one from remaining 4+3 points=5C2*(4+3)=70..
4) 1 point from each line containing 3,4,5 points =3*4*5=60..
total 27+48+70+60=205..


also you do not have to do the entire calculation in 12C3..
12C3=12!/3!9!= 12*11*10*9!/3!9!=12*11*10/3*2...
so you see you just have to multiply 12,11,and 10..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2618
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior  [#permalink]

Show Tags

New post 06 Mar 2016, 18:56
very nice question...tried to analyze it first..then did not how to solve it..went with chetan2u 's method..
we can have 1 point on from 3, 1 point from 4, 1 point from 5: 3C1*4C1*5C1 = 60
we can have 1 point from 3, and 2 points from 5 = 3C1*5C2 = 30
we can have 1 point from 3, and 2 points from 4 = 3C1*4C2 = 18
we can have 1 point from 4, and 2 points from 3 = 4C1*3C2 = 12
we can have 1 point from 4, and 2 points from 5 = 4C1*5C2 = 40
we can have 1 point from 5, and 2 points from 3 = 5C1*3C2 = 15
we can have 1 point from 5, and 2 points from 4 = 5C1*4C2 = 30

now total: 60+30+18+12+40+15+30 = 205
Manager
Manager
User avatar
B
Joined: 01 Jan 2018
Posts: 69
Re: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior  [#permalink]

Show Tags

New post 04 Aug 2018, 20:42
Hi, Can someone please clear my doubt- If we are joining three points ..one point from each side of original triangle then 4 triangles formed. Why we dont consider those triangles as well?

Sent from my Redmi Note 3 using GMAT Club Forum mobile app
_________________

+1 Kudos if you find this post helpful

Manager
Manager
User avatar
S
Joined: 19 Nov 2017
Posts: 174
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Re: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior  [#permalink]

Show Tags

New post 04 Aug 2018, 21:41
dvishal387 wrote:
Hi, Can someone please clear my doubt- If we are joining three points ..one point from each side of original triangle then 4 triangles formed. Why we dont consider those triangles as well?

Sent from my Redmi Note 3 using GMAT Club Forum mobile app


The triangles need to be formed from the interior points i.e. treating the interior points as vertices. This is mentioned in the question, just go back and have a look.
_________________

Regards,

Vaibhav



Sky is the limit. 800 is the limit.

~GMAC

Manager
Manager
User avatar
B
Joined: 01 Jan 2018
Posts: 69
Re: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior  [#permalink]

Show Tags

New post 04 Aug 2018, 22:45
vaibhav1221 wrote:
dvishal387 wrote:
Hi, Can someone please clear my doubt- If we are joining three points ..one point from each side of original triangle then 4 triangles formed. Why we dont consider those triangles as well?

Sent from my Redmi Note 3 using GMAT Club Forum mobile app


The triangles need to be formed from the interior points i.e. treating the interior points as vertices. This is mentioned in the question, just go back and have a look.
Okay..thanks

Sent from my Redmi Note 3 using GMAT Club Forum mobile app
_________________

+1 Kudos if you find this post helpful

GMAT Club Bot
Re: The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior &nbs [#permalink] 04 Aug 2018, 22:45
Display posts from previous: Sort by

The sides BC, CA, AB of triangle ABC have 3, 4, 5 interior

  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®.