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

It is currently 15 Jul 2018, 23:58

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

In the grid of dots above, each dot has equal vertical &

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

Hide Tags

Expert Post
2 KUDOS received
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4667
In the grid of dots above, each dot has equal vertical & [#permalink]

Show Tags

New post 20 Nov 2013, 17:05
2
12
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

59% (01:48) correct 41% (02:33) wrong based on 138 sessions

HideShow timer Statistics

Attachment:
half-square grid of dots with triangle.JPG
half-square grid of dots with triangle.JPG [ 15.11 KiB | Viewed 4199 times ]

In the grid of dots above, each dot has equal vertical & horizontal spacing from the others. A small 45-45-90 triangle is drawn. Counting this triangle, how many triangles congruent to this one, of any orientation, can be constructed from dots in this grid?
A. 112
B. 120
C. 240
D. 448
E. 480


For a discussion of difficult counting problems, as well as the solution to this problem, see:
http://magoosh.com/gmat/2013/difficult- ... -problems/

Mike :-)

_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Magoosh Discount CodesMath Revolution Discount CodesJamboree Discount Codes
Most Helpful Community Reply
3 KUDOS received
Current Student
avatar
Joined: 13 Aug 2013
Posts: 45
GMAT ToolKit User
Re: In the grid of dots above, each dot has equal vertical & [#permalink]

Show Tags

New post 26 Feb 2015, 00:33
3
2
Attachment:
half-square grid of dots with triangle.JPG
half-square grid of dots with triangle.JPG [ 19 KiB | Viewed 3490 times ]


Count the number of possible squares (just as the one highlighted above) in figure = 28
Each such square can contain 4 triangles = 28 x 4 = 112.

On the diagonal of the half square we can have another 8 triangles.

So total number of triangles = 112 + 8 = 120
_________________

Kudos plz if it helped

General Discussion
1 KUDOS received
Intern
Intern
avatar
Joined: 06 Sep 2013
Posts: 14
Re: In the grid of dots above, each dot has equal vertical & [#permalink]

Show Tags

New post 21 Nov 2013, 13:27
1
mikemcgarry wrote:
Attachment:
half-square grid of dots with triangle.JPG

In the grid of dots above, each dot has equal vertical & horizontal spacing from the others. A small 45-45-90 triangle is drawn. Counting this triangle, how many triangles congruent to this one, of any orientation, can be constructed from dots in this grid?
A. 112
B. 120
C. 240
D. 448
E. 480


For a discussion of difficult counting problems, as well as the solution to this problem, see:
http://magoosh.com/gmat/2013/difficult- ... -problems/

Mike :-)


well, sorry that i cant draw any pictures to illustrate but i will try my best to explain with word.
Here is my approach: think of the distance between each dot as 1 unit, i try to image there is a square whose sides are 1 unit. When I try to count all those qualified squares. there are 28 of them. And in each such square, there are 4 ways to place the triangle under the 45-45-90 condition. So there are 28*4=112 of them, plus the left triangles which cannot form a square but also qualify, they are located at the right end from top to bottom, so we get another 8 of those triangles. In total 112+8=120
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2726
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
In the grid of dots above, each dot has equal vertical & [#permalink]

Show Tags

New post 16 May 2016, 20:09
mikemcgarry wrote:
Attachment:
half-square grid of dots with triangle.JPG

In the grid of dots above, each dot has equal vertical & horizontal spacing from the others. A small 45-45-90 triangle is drawn. Counting this triangle, how many triangles congruent to this one, of any orientation, can be constructed from dots in this grid?
A. 112
B. 120
C. 240
D. 448
E. 480


For a discussion of difficult counting problems, as well as the solution to this problem, see:
http://magoosh.com/gmat/2013/difficult- ... -problems/

Mike :-)


good question...i almost started to count all possible 45-45-90 triangles that can be drawn..but since we need congruent...the task is easier...
we have 7, 6, 5, 4, 3, 2, 1 - squares that can be created using the dots. in which square, we can have 4 variations of the triangle.
sum of 7 = 7*8/2 = 7*4=28
now, 28*4 = 112. we can eliminate A right away, as we did not count the "outer" possible triangles.
we can draw 8 triangles with the "outer" points.
112+8=120.

B

p.s. is there a way to count all possible variations of 45-45-90 triangle??? I believe it should be possible using the similar method..but would take way too much to solve..
Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6201
Re: In the grid of dots above, each dot has equal vertical & [#permalink]

Show Tags

New post 16 May 2016, 20:51
mvictor wrote:
mikemcgarry wrote:
Attachment:
half-square grid of dots with triangle.JPG

In the grid of dots above, each dot has equal vertical & horizontal spacing from the others. A small 45-45-90 triangle is drawn. Counting this triangle, how many triangles congruent to this one, of any orientation, can be constructed from dots in this grid?
A. 112
B. 120
C. 240
D. 448
E. 480


For a discussion of difficult counting problems, as well as the solution to this problem, see:
http://magoosh.com/gmat/2013/difficult- ... -problems/

Mike :-)


good question...i almost started to count all possible 45-45-90 triangles that can be drawn..but since we need congruent...the task is easier...
we have 7, 6, 5, 4, 3, 2, 1 - squares that can be created using the dots. in which square, we can have 4 variations of the triangle.
sum of 7 = 7*8/2 = 7*4=28
now, 28*4 = 112. we can eliminate A right away, as we did not count the "outer" possible triangles.
we can draw 8 triangles with the "outer" points.
112+8=120.

B

p.s. is there a way to count all possible variations of 45-45-90 triangle??? I believe it should be possible using the similar method..but would take way too much to solve..


Hi,

ONE way I can think of is -


Look at the Hypotenuse...
the outermost has 9 dots and there on keeps reducing by 1 for each slant line below it..
the outermost cannot make any 45-45-90 triangles..
the second line has 8 dots and each dot can make ONE triangle with the outer most HYP= 8*1..
the Third line has 7 dots and each dot can make TWO triangle with the two hypotenuse outside= 7*2..
similarily 1 dots and that can make 8 triangles with 8 HYP= 1*8...
TOTAL = \(8*1+7*2+6*3+5*4+4*5+3*6+2*7+1*8 = 2 ( 8*1+7*2+6*3+5*4 ) = 2(8+14+18+20) = 2*60 = 120\)
_________________

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

Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 980
Re: In the grid of dots above, each dot has equal vertical & [#permalink]

Show Tags

New post 26 Jun 2016, 08:17
mikemcgarry wrote:
Attachment:
The attachment half-square grid of dots with triangle.JPG is no longer available

In the grid of dots above, each dot has equal vertical & horizontal spacing from the others. A small 45-45-90 triangle is drawn. Counting this triangle, how many triangles congruent to this one, of any orientation, can be constructed from dots in this grid?
A. 112
B. 120
C. 240
D. 448
E. 480


For a discussion of difficult counting problems, as well as the solution to this problem, see:
http://magoosh.com/gmat/2013/difficult- ... -problems/

Mike :-)

a four dots will contribute to 4 congruent trangles as shown taking each set os dots as a new base
secondly every extreme right side 3 dots will form only 1 triangle
first row will make 1 triangle
second row will make 4+1=5 triangle
third row =9 triangles
a pattern here is every new row will add 4 new triangles.
there are 8 rows
total triangles=(1+5+9+....29)=120
Ans B
Attachments

half-square grid of dots with triangle.JPG
half-square grid of dots with triangle.JPG [ 25.36 KiB | Viewed 2908 times ]

Intern
Intern
avatar
B
Joined: 09 Dec 2016
Posts: 14
Concentration: Leadership, General Management
Schools: ISB '19 (D)
Re: In the grid of dots above, each dot has equal vertical & [#permalink]

Show Tags

New post 13 Sep 2017, 23:57
Why bigger triangles are not considered in this? Does congruent means equal? I thought it to be similar triangle.
Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4667
Re: In the grid of dots above, each dot has equal vertical & [#permalink]

Show Tags

New post 14 Sep 2017, 16:16
1
ashokjha1986 wrote:
Why bigger triangles are not considered in this? Does congruent means equal? I thought it to be similar triangle.

Dear ashokjha1986,

i'm happy to respond. :-)

These are good terms to know, as a GMAT Quant problem might mention them:
1) congruent = same shape, same size (equal angles, equal lengths)
2) similar = same shape, different size (equal angles, proportional lengths)

Does this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Re: In the grid of dots above, each dot has equal vertical &   [#permalink] 14 Sep 2017, 16:16
Display posts from previous: Sort by

In the grid of dots above, each dot has equal vertical &

  new topic 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®.