BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Polygon

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

Polygon

by harsh.champ » Thu Feb 04, 2010 1:57 pm
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
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Thu Feb 04, 2010 2:09 pm
harsh.champ 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
I got 21 by drawing it out (in under 2 minutes), but that's not a very scientific approach (which doesn't mean it's a bad approach; you get graph lined scratch paper on the GMAT, so if you can visualize the shape it's a good way to tackle the question).

If you draw out some simpler shapes, you can quickly see that convex - concave will always equal 4. I'm sure that someone has a beautiful proof for this deduction, but it's certainly not one you'd ever need to know for the GMAT.

What's the source of this question?
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Thu Feb 04, 2010 2:19 pm
harsh.champ 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
The angles in an n-sided polygon add to (n-2)*180. If we have 25 angles measuring 90 degrees, and x angles measuring 270 degrees, then we have 25+x sides in total, so

(25 + x - 2)(180) = 25*90 + 270*x
(23 + x)(180) = 90(25 + 3x)
(23 + x)(2) = 25 + 3x
46 + 2x = 25 + 3x
x = 21
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Thu Feb 04, 2010 2:24 pm
Stuart Kovinsky wrote: If you draw out some simpler shapes, you can quickly see that convex - concave will always equal 4. I'm sure that someone has a beautiful proof for this deduction, but it's certainly not one you'd ever need to know for the GMAT.
Yes, that will be true in general; in an n-sided shape, the sum of our angles is 180n - 360. If we have only 'x' 90 degree angles and 'y' 270 degree angles in our shape, we have x+y angles in total, and we need 90x + 270y to be equal to 180x + 180y - 360. So you might be able to see immediately that we need x to be 4 more than y to account for the '-360' part; or we can prove this algebraically:

90x + 270y = 180x + 180y - 360
x + 3y = 2x + 2y - 4
x - y = 4
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Thu Feb 04, 2010 2:51 pm
Stuart Kovinsky wrote:
harsh.champ wrote: (5)23
I got 21 by drawing it out (in under 2 minutes), but that's not a very scientific approach (which doesn't mean it's a bad approach; you get graph lined scratch paper on the GMAT, so if you can visualize the shape it's a good way to tackle the question).

If you draw out some simpler shapes, you can quickly see that convex - concave will always equal 4. I'm sure that someone has a beautiful proof for this deduction, but it's certainly not one you'd ever need to know for the GMAT.

What's the source of this question?
_____________
This question is a part of the test given by a tutor at my native place.
Actually,now I am a bit confused as to what concepts are not necessary for GMAT preparation and what concepts are indispensable.I thought this was supposed to be a good geometry problem.
Please can you throw some light if I am doing some mistake in my preparation strategy!!!
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Thu Feb 04, 2010 3:02 pm
harsh.champ wrote:
_____________
This question is a part of the test given by a tutor at my native place.
Actually,now I am a bit confused as to what concepts are not necessary for GMAT preparation and what concepts are indispensable.I thought this was supposed to be a good geometry problem.
Please can you throw some light if I am doing some mistake in my preparation strategy!!!
If you're preparing for the GMAT, you should focus on the types of questions that are going to show up on the actual exam. If your tutor is a math expert but not familiar with the GMAT, then he or she isn't a good person to be giving you questions.

While it's true that working on challenging questions will help you improve, those questions need to be relevant to the GMAT. Most test takers only see 3-5 geometry questions in total and those questions focus primarily on basic geometry. Of course if you're doing great on the GMAT you'll see more advanced applications of those basic principles, but it's the basic principles you need to master.

If you don't already have it, buy the Official Guide and review the preview math chapters to get a feel for the level of math on which you'll be tested.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Thu Feb 04, 2010 3:10 pm
Stuart Kovinsky wrote:
harsh.champ wrote:
_____________
This question is a part of the test given by a tutor at my native place.
Actually,now I am a bit confused as to what concepts are not necessary for GMAT preparation and what concepts are indispensable.I thought this was supposed to be a good geometry problem.
Please can you throw some light if I am doing some mistake in my preparation strategy!!!
If you're preparing for the GMAT, you should focus on the types of questions that are going to show up on the actual exam. If your tutor is a math expert but not familiar with the GMAT, then he or she isn't a good person to be giving you questions.

While it's true that working on challenging questions will help you improve, those questions need to be relevant to the GMAT. Most test takers only see 3-5 geometry questions in total and those questions focus primarily on basic geometry. Of course if you're doing great on the GMAT you'll see more advanced applications of those basic principles, but it's the basic principles you need to master.

If you don't already have it, buy the Official Guide and review the preview math chapters to get a feel for the level of math on which you'll be tested.
_____________________
Thanks for the advice.
I have the OG 12th edition and i use it from time to time.
Actually,the tutor's mentality is to prepare us even for tough questions.Though most questions tested on the GMAT are of a far easier variety but that puts us in a comfortable state having solved the advanced ones.
As on the GMAT,you can't skip any question,he said that you should have the level of preparation a notch higher than the question level that you will expect on the D-Day.
I have reviewed the math chapters of the OG and have got a cetain feel about the kind of questions featured.
If my basics are strong,is it Ok to skip that section and move to my weaker sections or should I maintain equivalent level of efforts in all the sections??Right now,I am pursuing the latter.
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Thu Feb 04, 2010 3:29 pm
harsh.champ wrote: _____________________
Thanks for the advice.
I have the OG 12th edition and i use it from time to time.
Actually,the tutor's mentality is to prepare us even for tough questions.Though most questions tested on the GMAT are of a far easier variety but that puts us in a comfortable state having solved the advanced ones.
As on the GMAT,you can't skip any question,he said that you should have the level of preparation a notch higher than the question level that you will expect on the D-Day.
I have reviewed the math chapters of the OG and have got a cetain feel about the kind of questions featured.
If my basics are strong,is it Ok to skip that section and move to my weaker sections or should I maintain equivalent level of efforts in all the sections??Right now,I am pursuing the latter.
If you're comfortable with the math in general, you should start with intermediate questions (the ones you'll see at the beginning of the test) and then progress to advanced questions. One common mistake that people make is to ignore the intermediate questions; a common result of this is that they're baffled by the first few questions in each section and never get to the advanced questions for which they're prepared.

For your overall studies, if you're particularly weaker on one type of question, then I'd give that area more attention as you're starting out. However, more attention certainly doesn't mean all of your attention; work on all the areas on the exam to keep your momentum going and to pick up points in a variety of areas.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Post new topic Post Reply
• Page 1 of 1