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

 It is currently 02 Jul 2015, 13:50

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A elderly man, in order to practise manual dexterity, draws

Author Message
TAGS:
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1266
Followers: 24

Kudos [?]: 167 [0], given: 0

A elderly man, in order to practise manual dexterity, draws [#permalink]  25 Jul 2006, 00:57
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
A elderly man, in order to practise manual dexterity, draws 50 triangles a day by connecting three of the solid points on the grid made up of 16 squares shown in the attachment. He starts this activity on January 1 and is careful not to skip a day. On which day will he be forced to retrace one of his previously drawn triangles?

(A) February 12 (B) February 13 (C) February 14 (D) February 15 (E) None of these
Attachments

elderly pastime.doc [23.5 KiB]

Director
Joined: 13 Nov 2003
Posts: 790
Location: BULGARIA
Followers: 1

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

Think it is like that
Total number of selecting 3 poins out of 25 is 2300 triplets. Now remove 5C3*10 for the colinear triplets in vertical and horizontal lines of the grid. Remove 5C3*2 for the 2 diagonals 4C3*4 for the lines parallel to the diagonals, and finally 3C3 for the outer parallel lines to the diagonals. In total we have: 2300-( 100+20+16+4)=>2160 triangles. divide by 20 to find in how many days the different triangles will be depleted.
Senior Manager
Joined: 11 Jul 2006
Posts: 383
Location: TX
Followers: 1

Kudos [?]: 6 [0], given: 0

As shown in the figure there are (5*5)25 distinct points in the figure.
To draw each triangle you need 3 distinct points.
He cannot retrace a line already drawn. It means that he cannot select a combination of points for a line which has already been selected.

Now , you as look at this problen as follows
How many ways you can select a combination of 3 points from 25 points ?
Using the formula for Combination
25!
--------- = 2300 , So he can draw 2300 triangles without retracing.
3!(25-3)!

Old man draws 50 triangles a day , so he will need 46 days.
January has 31 days , So he would finish drawing all possible triangles by Feb 15th. On the 16th he would have to retrace . Hence E
SVP
Joined: 30 Mar 2006
Posts: 1737
Followers: 1

Kudos [?]: 46 [0], given: 0

In each square there are 4 points. YOu can join three points to make 3 triangles.

hence with 16 squares you can make 16*3 = 48 triangles.

Hence in the 49th day he will be forced to retrace one of the triangles.

49th day is not one of the options. Hence E
Director
Joined: 13 Nov 2003
Posts: 790
Location: BULGARIA
Followers: 1

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

SInce he is drawing 50 triangles a day, and can draw 2160 triangles then in January he will have drawn 50*31=1550 triangles. He has 12 more days to draw different triangles, and on 13 of February he will start redrawing his triangles.
So the ans is B
Intern
Joined: 21 Jul 2006
Posts: 27
Followers: 0

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

_________________

Be Supportive and Helpful! And Everything Will Bounce Back to You!

GMAT Instructor
Joined: 04 Jul 2006
Posts: 1266
Followers: 24

Kudos [?]: 167 [0], given: 0

I thank you for your patience. I want somebody to have the pleasure of solving it. BG is close...
CEO
Joined: 20 Nov 2005
Posts: 2910
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 19

Kudos [?]: 132 [0], given: 0

Total triangles possible = 25C3 - 10 * 5C3 = 2200

Total days = 2200/50 = 44
He will finish on Feb 13
On Feb 14 he is forced to redraw.

_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Director
Joined: 28 Dec 2005
Posts: 755
Followers: 1

Kudos [?]: 8 [0], given: 0

25 points. 3 needed to make a triangle

Ways of choosing 3 pts = 25c3
invalid cases (3 pts on same line) = 10 x 5c3

triangles = 25c3 - 10x5c3 = 2200

days these will last = 2200/50 = 44

Jan has 31 days so 13 left in feb.

on 14th feb, he will reuse. C?
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1266
Followers: 24

Kudos [?]: 167 [0], given: 0

BG is closer, but you're on the right track!
Director
Joined: 28 Dec 2005
Posts: 755
Followers: 1

Kudos [?]: 8 [0], given: 0

Ok i figured some more stuff....

25C3 = 2300

Number of straight lines with 5 points = 12 (gives 12x5c3 = 120)
number of straight lines with 4 points = 4 (gives 4x4c3 = 16)
'' 3 '' = 16 (give 16x3c3 = 16)

So subtract 152 from 2300 and we get 2148

2148/50 = 42 days => 11 days in feb so feb 12th he will restart? A?
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1266
Followers: 24

Kudos [?]: 167 [0], given: 0

ps_dahiya wrote:
Futuristic wrote:
'' 3 '' = 16

where are 16???

One is from top centre to bottom left. Did you like this question?
Director
Joined: 28 Dec 2005
Posts: 755
Followers: 1

Kudos [?]: 8 [0], given: 0

The 16 lines with 3 points is the tricky part. Since I don't have the time to draw it out consider the grid to be extending from 0,0 into the 1st quadrant of the xy plane only. Now the following sets of co-ordinates will define lines having exactly 3 points in the grid.

1. (0,0), (2,4)
2. (1,0), (3,4)
3. (2,0), (4,4)

Rotate the grid by 90 degrees and you'll get 3 more unique lines in the grid for a total of 12.

For the remaining 4 lines, consider the following co-ordinates

1. (0,2),(2,4)
2. (2,0),(4,2)

In this case, you will find there are 4 unique lines.

Hope this clarifies it. kevin this was a killer. i hope you don't ever get to set a gmat paper!
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1266
Followers: 24

Kudos [?]: 167 [0], given: 0

Thanks to everybody who tried this. Shall I make it easier for my book?
Similar topics Replies Last post
Similar
Topics:
Probability-Draw a King and Queen 2 15 Jun 2011, 21:40
A elderly man, in order to practise manual dexterity, draws 1 17 Sep 2006, 13:55
The above drawing is of a wooden paperweight that will be 6 14 Sep 2006, 02:22
In the drawing attached, the shaded region is bound by the 5 16 Jul 2006, 15:07
The drawing on the left is of a gold pendant of uniform 1 15 Jul 2006, 11:25
Display posts from previous: Sort by