Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions)
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 25 Aug 2007
Posts: 673
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
Updated on: 14 Oct 2013, 01:34
Question Stats:
56% (02:29) correct 44% (02:05) wrong based on 144 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?).
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Originally posted by ykaiim on 16 Apr 2010, 06:12.
Last edited by Bunuel on 14 Oct 2013, 01:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




Current Student
Joined: 06 Sep 2013
Posts: 33
Location: India
Concentration: Leadership, Strategy
GPA: 3.7
WE: Information Technology (Consulting)

Re: Polygon with concave and convex corners
[#permalink]
Show Tags
14 Oct 2013, 01:13
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 +y2).
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.




Manager
Joined: 18 Mar 2010
Posts: 71
Location: United States

Re: Polygon with concave and convex corners
[#permalink]
Show Tags
19 Apr 2010, 15:04
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.



SVP
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2496
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: Polygon with concave and convex corners
[#permalink]
Show Tags
19 Apr 2010, 15:16
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 fightMoney Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership  big benefits and savingsGmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Intern
Joined: 29 Apr 2010
Posts: 2

Each side of a given polygon is parallel to either the X or
[#permalink]
Show Tags
29 Apr 2010, 05:10
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
Joined: 20 Apr 2010
Posts: 131
Location: I N D I A

Re: polygon
[#permalink]
Show Tags
29 Apr 2010, 06:17
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 421 times



Manager
Joined: 24 Jul 2009
Posts: 209

Re: polygon
[#permalink]
Show Tags
29 Apr 2010, 06:44
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(n2). 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
Joined: 25 Oct 2013
Posts: 142

Re: Polygon with concave and convex corners
[#permalink]
Show Tags
14 Feb 2014, 05:58
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 +y2).
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
Joined: 09 Jun 2015
Posts: 90

Each side of a given polygon is parallel to either the X or
[#permalink]
Show Tags
14 Mar 2016, 23:25
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
Joined: 14 Jul 2014
Posts: 158
Location: United States
GMAT 1: 600 Q48 V27 GMAT 2: 720 Q50 V37
GPA: 3.2

Re: Each side of a given polygon is parallel to either the X or
[#permalink]
Show Tags
05 May 2016, 12:53
My equations: 180(n  2) = 25(90) + 270(n  25). Ended up with: 90(46) = 90n
n = 46, n  25 = 21. Answer is 21.



NonHuman User
Joined: 09 Sep 2013
Posts: 13168

Re: Each side of a given polygon is parallel to either the X or
[#permalink]
Show Tags
03 May 2019, 06:26
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.
_________________




Re: Each side of a given polygon is parallel to either the X or
[#permalink]
03 May 2019, 06:26






