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

It is currently 20 Feb 2019, 08:17

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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Prep Hour

     February 20, 2019

     February 20, 2019

     08:00 PM EST

     09:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

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

 
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4486
In the grid of dots above, each dot has equal vertical &  [#permalink]

Show Tags

New post 20 Nov 2013, 16:05
2
13
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

54% (02:32) correct 46% (02:39) wrong based on 159 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 5449 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


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

Most Helpful Community Reply
Intern
Intern
avatar
Joined: 13 Aug 2013
Posts: 43
GMAT ToolKit User
Re: In the grid of dots above, each dot has equal vertical &  [#permalink]

Show Tags

New post 25 Feb 2015, 23:33
5
2
Attachment:
half-square grid of dots with triangle.JPG
half-square grid of dots with triangle.JPG [ 19 KiB | Viewed 4735 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
Intern
Intern
avatar
Joined: 06 Sep 2013
Posts: 11
Re: In the grid of dots above, each dot has equal vertical &  [#permalink]

Show Tags

New post 21 Nov 2013, 12:27
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: 2587
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, 19:09
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..
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Re: In the grid of dots above, each dot has equal vertical &  [#permalink]

Show Tags

New post 16 May 2016, 19:51
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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

VP
VP
User avatar
P
Joined: 05 Mar 2015
Posts: 1001
Re: In the grid of dots above, each dot has equal vertical &  [#permalink]

Show Tags

New post 26 Jun 2016, 07:17
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 4152 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, 22:57
Why bigger triangles are not considered in this? Does congruent means equal? I thought it to be similar triangle.
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4486
Re: In the grid of dots above, each dot has equal vertical &  [#permalink]

Show Tags

New post 14 Sep 2017, 15:16
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


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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9861
Premium Member
Re: In the grid of dots above, each dot has equal vertical &  [#permalink]

Show Tags

New post 01 Oct 2018, 11:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: In the grid of dots above, each dot has equal vertical &   [#permalink] 01 Oct 2018, 11:41
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  


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®.