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

It is currently 17 Dec 2018, 06:40

R1 Decisions:

Michigan Ross Chat (US calls are expected today)  |  UCLA Anderson Chat  (Calls expected to start at 7am PST; Applicants from Asia will hear first)


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
  • 10 Keys to nail DS and CR questions

     December 17, 2018

     December 17, 2018

     06:00 PM PST

     07:00 PM PST

    Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong.
  • R1 Admission Decisions: Estimated Decision Timelines and Chat Links for Major BSchools

     December 17, 2018

     December 17, 2018

     10:00 PM PST

     11:00 PM PST

    From Dec 5th onward, American programs will start releasing R1 decisions. Chat Rooms: We have also assigned chat rooms for every school so that applicants can stay in touch and exchange information/update during decision period.

Each side of a given polygon is parallel to either the X or

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

Hide Tags

Director
Director
User avatar
Joined: 24 Aug 2007
Posts: 754
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Each side of a given polygon is parallel to either the X or  [#permalink]

Show Tags

New post Updated on: 14 Oct 2013, 00:34
1
13
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

55% (02:31) correct 45% (02:05) wrong based on 176 sessions

HideShow timer Statistics

Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°. If the number of convex corners in such a polygon is 25, the number of concave corners must be:

(A) 20
(B) 0
(C) 21
(D) 22
(E) 23

3. 21
In this kind of polygon, the number of convex angles will always be exactly 4 more
than the number of concave angles (why?).

_________________

Want to improve your CR: http://gmatclub.com/forum/cr-methods-an-approach-to-find-the-best-answers-93146.html
Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html
Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html


Originally posted by ykaiim on 16 Apr 2010, 05:12.
Last edited by Bunuel on 14 Oct 2013, 00:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Most Helpful Community Reply
Intern
Intern
avatar
B
Joined: 06 Sep 2013
Posts: 33
Location: India
Concentration: Leadership, Strategy
Schools: ISB '19 (A)
GMAT 1: 770 Q50 V44
GPA: 3.7
WE: Information Technology (Consulting)
Re: Polygon with concave and convex corners  [#permalink]

Show Tags

New post 14 Oct 2013, 00:13
7
Let the number of convex corner be x and the number of concave corners be y.
Therfore the sum of the angles of the polygon would be 90*x +270*y.

Also the sum of the angles can also be given by 180*(x +y-2).

Therefore,
90*x + 270*y = 180*(x + y - 2)
or, 90*x - 90*y = 360
or x - y = 4.

Therefore if x = 25, y = 21.
General Discussion
Manager
Manager
avatar
Joined: 18 Mar 2010
Posts: 85
Location: United States
Re: Polygon with concave and convex corners  [#permalink]

Show Tags

New post 19 Apr 2010, 14:04
I had to visualize this one. In a polygon with sides parallel to the x or y axis, the smallest number of sides would be four, making a rectangle (4 concave corners, 0 convex corners). As you "add" corners, you can do it one of two ways: either by taking a "bite" out of a corner taking away one concave corner, and replacing it with one convex corner and two concave corners, or taking a bite out of a side adding two concave and two convex corners. Either way, you are still add a 1:1 ratio of corners with each addition, plus the four corners you had at the beginning.So you will always have four more concave corners than convex corners.

If there is a mathmatical way to figure this out I would love to hear it, but visuallizing it in this way is the fastest way I can think of.
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2595
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: Polygon with concave and convex corners  [#permalink]

Show Tags

New post 19 Apr 2010, 14:16
mmphf wrote:
I had to visualize this one. In a polygon with sides parallel to the x or y axis, the smallest number of sides would be four, making a rectangle (4 concave corners, 0 convex corners). As you "add" corners, you can do it one of two ways: either by taking a "bite" out of a corner taking away one concave corner, and replacing it with one convex corner and two concave corners, or taking a bite out of a side adding two concave and two convex corners. Either way, you are still add a 1:1 ratio of corners with each addition, plus the four corners you had at the beginning.So you will always have four more concave corners than convex corners.

If there is a mathmatical way to figure this out I would love to hear it, but visuallizing it in this way is the fastest way I can think of.


visualizing is the best way. :)

pls check the bolded text above, it should be vice versa
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Intern
avatar
Joined: 29 Apr 2010
Posts: 2
Each side of a given polygon is parallel to either the X or  [#permalink]

Show Tags

New post 29 Apr 2010, 04:10
1
1
Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90o or concave if the internal angle is 270o. If the number of convex corners in such a polygon is 25, the number of concave corners must be:

(1)20
(2)0
(3)21
(4)22
(5)23
Manager
Manager
avatar
Joined: 20 Apr 2010
Posts: 134
Location: I N D I A
Re: polygon  [#permalink]

Show Tags

New post 29 Apr 2010, 05:17
I also think the answer is 21...

In the figure attached

1,2,3,4 so on represent convex angles...

1`,2`,3`... so on represent concave angles... which will be 21..
Attachments

Angles.doc [24.5 KiB]
Downloaded 391 times

To download please login or register as a user

Manager
Manager
avatar
Joined: 24 Jul 2009
Posts: 244
Re: polygon  [#permalink]

Show Tags

New post 29 Apr 2010, 05:44
5
lanka1 wrote:
Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90o or concave if the internal angle is 270o. If the number of convex corners in such a polygon is 25, the number of concave corners must be:

(1)20
(2)0
(3)21
(4)22
(5)23



Sum of all the angles is 180(n-2).
Let the total no of 90 deg angle be x
Let the total no of 270 deg angle be y

n= x+y, so sum of all the angles is 180(x+y -2)

so, 90x + 270y = 180(x+y -2)
90x + 270y = 180x+ 180y - 360
90y = 90x -360

Given x=25
y= (90*25 - 360)/90
y= 21
Manager
Manager
avatar
Joined: 25 Oct 2013
Posts: 151
Re: Polygon with concave and convex corners  [#permalink]

Show Tags

New post 14 Feb 2014, 04:58
Yes, this seems to be the best way to solve the problem. I tried to visualize the polygon and ended up with correct answer as 21.

End deduction was that the number of convex corners of such polygon are always 4 more than number of concave corners of the same polygon.

nitesh181989 wrote:
Let the number of convex corner be x and the number of concave corners be y.
Therfore the sum of the angles of the polygon would be 90*x +270*y.

Also the sum of the angles can also be given by 180*(x +y-2).

Therefore,
90*x + 270*y = 180*(x + y - 2)
or, 90*x - 90*y = 360
or x - y = 4.

Therefore if x = 25, y = 21.

_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Manager
Manager
avatar
Joined: 09 Jun 2015
Posts: 93
Each side of a given polygon is parallel to either the X or  [#permalink]

Show Tags

New post 14 Mar 2016, 22:25
ykaiim wrote:
Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°. If the number of convex corners in such a polygon is 25, the number of concave corners must be:

(A) 20
(B) 0
(C) 21
(D) 22
(E) 23

3. 21
In this kind of polygon, the number of convex angles will always be exactly 4 more
than the number of concave angles (why?).

It is because of the geometric pattern.
for a square you have 4 convex corners.
If you want to increase the number of sides you have to make an opening on one side. When you open one hole and draw lines parallel to x and y axis, it adds 2 convex and 2 concave corners (check it!). This pattern goes on on and makes a difference of 4, like, (4,0), (6,2), (8,4) and so on.
Manager
Manager
avatar
B
Joined: 14 Jul 2014
Posts: 174
Location: United States
Schools: Duke '20 (D)
GMAT 1: 600 Q48 V27
GMAT 2: 720 Q50 V37
GPA: 3.2
Reviews Badge
Re: Each side of a given polygon is parallel to either the X or  [#permalink]

Show Tags

New post 05 May 2016, 11:53
1
My equations: 180(n - 2) = 25(90) + 270(n - 25).
Ended up with: 90(46) = 90n

n = 46, n - 25 = 21.
Answer is 21.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9197
Premium Member
Re: Each side of a given polygon is parallel to either the X or  [#permalink]

Show Tags

New post 26 Feb 2018, 06:49
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: Each side of a given polygon is parallel to either the X or &nbs [#permalink] 26 Feb 2018, 06:49
Display posts from previous: Sort by

Each side of a given polygon is parallel to either the X or

  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®.