Find all School-related info fast with the new School-Specific MBA Forum

It is currently 03 Sep 2015, 20:31
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The measures of the interior angles in a polygon are

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 552
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V40
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 38

Kudos [?]: 1388 [1] , given: 217

The measures of the interior angles in a polygon are [#permalink] New post 11 Feb 2012, 15:07
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

65% (03:07) correct 35% (02:15) wrong based on 91 sessions
The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?

A) 8
B) 9
C) 10
D) 11
E) 13

Please help.
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Expert Post
4 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 629
Followers: 64

Kudos [?]: 776 [4] , given: 135

Premium Member
Re: The measures of the interior angles in a polygon are [#permalink] New post 17 Apr 2013, 01:02
4
This post received
KUDOS
Expert's post
enigma123 wrote:
The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?

A) 8
B) 9
C) 10
D) 11
E) 13

Please help.

Just another way of doing this sum:
The sum of exterior angles for any polygon = 360 degrees.Now, given that the minimum internal angle measure is 136 degrees--> the exterior angle = 180-136 = 44 degrees.
Also, we know that this value will keep decreasing like 43,42,41 etc. It is easy to see that only if there 9 terms, the middle value is 40 and we know that 40*9 =360 degrees.

B.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29205
Followers: 4751

Kudos [?]: 50291 [2] , given: 7540

Re: Sides of a Polygon. [#permalink] New post 11 Feb 2012, 15:10
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
enigma123 wrote:
The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?

A) 8
B) 9
C) 10
D) 11
E) 13

Please help.


Sum of Interior Angles of a polygon is \(180(n-2)\) where \(n\) is the number of sides (so is the number of angles);

We are told that the smallest angle is 136 degrees, the next will be 136+1 degrees, ..., and the largest one, \(n_{th}\) angle, will be \(136+(n-1)\) degrees. The sum of the \(n\) consecutive integers (the sum of \(n\) angles) is given by \(\frac{first+last}{2}*# \ of \ terms=\frac{136+(136+n-1)}{2}*n=\frac{271+n}{2}*n\);

So we have that \(180(n-2)=\frac{271+n}{2}*n\) --> \(360(n-2)=(271+n)*n\), now try the answer choices: in order RHS to end with zero (as LHS is because of 360) then \(n\), out of the options listed, could be either 10 or 9, \(n=9\) fits.

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Manager
Manager
avatar
Joined: 10 Jan 2011
Posts: 244
Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 29 [1] , given: 25

Reviews Badge
Re: The measures of the interior angles in a polygon are [#permalink] New post 17 Apr 2013, 01:36
1
This post received
KUDOS
Another way of solving the problem

sum of internal angles of a polygon = (n-2)*180. as sum is multiplied by 180, the unit degit of sum should be 0.

also looking at the options least number of sides is 8.

sum of unit degits for 8 sides is 6 (from 136) + 7+8+9+0+1+2+3 = 6.
sum of unit degist for 9 sides is 6+7+8+9+0+1+2+3+4 = 0.
Hnec option B is correct anser
_________________

-------Analyze why option A in SC wrong-------

1 KUDOS received
Manager
Manager
avatar
Joined: 07 May 2013
Posts: 109
Followers: 0

Kudos [?]: 14 [1] , given: 1

Re: The measures of the interior angles in a polygon are [#permalink] New post 14 Nov 2013, 20:06
1
This post received
KUDOS
Remember that sum of angles in a polygon=(n-2)180. This means that whatever the value of n there will always be a 0 in units digit. Now, the question becomes 'How many consecutive integers we should add starting from 136 so that units digit is 0. 6+7+8+9+0=(3)0. Note that 3 is put in brackets bcos it is carried over. Now we know that sum of angles in a pentagon=540. But does 136+137+....140 equal 540. Use formula \(\frac{n}{2}\)(a+l)=\(\frac{5}{2}\)*(136+140)=690. Does not match. So proceed further. 6+7+8+9+0+1+2+3+4=(4)0. Now the series becomes 136+137+138+........+144 consisting of (144-136+1=)9 elements. Again use above formula for sum and it comes out to be 1260. Now we know that sum of angles in a nonagon is (n-2)180=1260. This choice matches. So, answer is 9.
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 552
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V40
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 38

Kudos [?]: 1388 [0], given: 217

Re: The measures of the interior angles in a polygon are [#permalink] New post 12 Feb 2012, 15:09
Buneul - how did you get that largest angle will be 136+n-1 degrees?
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Manager
Manager
avatar
Joined: 31 Jan 2012
Posts: 74
Followers: 2

Kudos [?]: 17 [0], given: 2

Re: The measures of the interior angles in a polygon are [#permalink] New post 12 Feb 2012, 19:35
He's using the average formula. Average uses the first and last number of an evenly spaced sequence. Since 136 is the smallest integer in the sequence it is one of the numbers. The largest number in the sequence since it's consecutive is 135+n or 136+(n-1). Lets n was one then. The answer would be 135+n which is equal to one, which is our smallest number. Let's say n (#of sides) is 4 then the largest number in the sequence will be 135+4= 139
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29205
Followers: 4751

Kudos [?]: 50291 [0], given: 7540

Re: The measures of the interior angles in a polygon are [#permalink] New post 13 Feb 2012, 03:34
Expert's post
enigma123 wrote:
Buneul - how did you get that largest angle will be 136+n-1 degrees?


There are n angles (sides):
The smallest angle is 136 degrees;
Next (2nd) angle is 136+1 degrees;
...
nth angle is 136+(n-1) degrees.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Current Student
User avatar
Joined: 23 Oct 2010
Posts: 386
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 15

Kudos [?]: 208 [0], given: 73

GMAT ToolKit User
Re: The measures of the interior angles in a polygon are [#permalink] New post 24 Apr 2013, 22:54
sum of angles =180(n-2) where n is the number of sides
since we have consecutive angles, then median=mean

B n=9 ,then the sum of angles =180*7

the median of 9 consecutive integers is 140 (136 137 138 139 140 141 142 143 144)
the sum of consecutive integers is 140*9

180*7/140*9 =(20*9*7)/(20*7*9)= 1
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 32

Kudos [?]: 346 [0], given: 355

GMAT ToolKit User
Re: The measures of the interior angles in a polygon are [#permalink] New post 02 Jan 2014, 09:13
1
This post was
BOOKMARKED
enigma123 wrote:
The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?

A) 8
B) 9
C) 10
D) 11
E) 13

Please help.


Note that the formula for the sum of the angles of a polygon is (n-2)*180

Therefore, the sum of the angles must end in zero

Now, let's start adding until we get units digit zero and then check if it satisfies

136+137+138+139 = We get digit zero

But if we ply (4-2)(180) = 360 this obviously doesn't satisfy cause 136+137...+139 is more than 360. So let's keep trying

+141+142+143+144...another digit 0

Let's see we now have 9 numbers so 180*7 = 1260

We then grab the median of the consecutive integers which is 140*9 = 1260

It satisfies so answer is thus B

Hope it helps
Cheers!
J :)
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6205
Followers: 346

Kudos [?]: 71 [0], given: 0

Premium Member
Re: The measures of the interior angles in a polygon are [#permalink] New post 25 Jun 2015, 03:02
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

Re: The measures of the interior angles in a polygon are   [#permalink] 25 Jun 2015, 03:02
    Similar topics Author Replies Last post
Similar
Topics:
104 Experts publish their posts in the topic The measurements obtained for the interior dimensions of a imhimanshu 13 22 Sep 2013, 06:22
2 Experts publish their posts in the topic The measures of the interior angles in a polygon guerrero25 2 16 Apr 2013, 12:28
21 Experts publish their posts in the topic The measures of the interior angles in a polygon are rxs0005 15 03 Feb 2011, 14:45
Experts publish their posts in the topic If the sum of the interior angles of a regular polygon... pzazz12 6 05 Oct 2010, 04:40
Area of the Interior angles of Rectangle ? Snowingreen 2 09 Feb 2010, 16:34
Display posts from previous: Sort by

The measures of the interior angles in a polygon are

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.