Author 
Message 
TAGS:

Hide Tags

Director
Joined: 29 Nov 2012
Posts: 850

The logo of a certain corporation is in the shape of a polyg [#permalink]
Show Tags
08 Jan 2013, 21:30
2
This post received KUDOS
9
This post was BOOKMARKED
Question Stats:
75% (01:30) correct 25% (01:32) wrong based on 361 sessions
HideShow timer Statistics
The logo of a certain corporation is in the shape of a polygon, where all angles of a the polygon have equal measures. In the above figure V is one vertex of the polygon. If Y in degrees is the measure of an angle of the polygon and y=5x how many sides does the polygon have? A 5 B 6 C 10 D 12 E 30
Official Answer and Stats are available only to registered users. Register/ Login.
Attachments
Untitled.png [ 41.92 KiB  Viewed 6773 times ]
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html
Last edited by fozzzy on 09 Jan 2013, 07:13, edited 3 times in total.



VP
Joined: 02 Jul 2012
Posts: 1209
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: The logo of a corporation [#permalink]
Show Tags
08 Jan 2013, 22:41
7
This post received KUDOS
7
This post was BOOKMARKED
From figure., x + y = 180 6*x = 180 x = 30, y = 150 Let number of sides be "n", hence number of interior angles is also "n" Sum of all interior angles = 150*n Formula for sum of interior angles = 180*(n2) 180*(n2) = 150*n 30*n = 360 n = 360/30 = 12 Answer is D
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Director
Joined: 29 Nov 2012
Posts: 850

Re: The logo of a corporation [#permalink]
Show Tags
09 Jan 2013, 02:24
MacFauz wrote: From figure.,
x + y = 180 6*x = 180 x = 30, y = 150
Let number of sides be "n", hence number of interior angles is also "n" Sum of all interior angles = 150*n Formula for sum of interior angles = 180*(n2)
180*(n2) = 150*n 30*n = 360
n = 360/30 = 12
Answer is D How did you get that step, I'm really bad at geometry...
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



VP
Joined: 02 Jul 2012
Posts: 1209
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: The logo of a corporation [#permalink]
Show Tags
09 Jan 2013, 02:29
1
This post received KUDOS
fozzzy wrote: MacFauz wrote: From figure.,
x + y = 180 6*x = 180 x = 30, y = 150
Let number of sides be "n", hence number of interior angles is also "n" Sum of all interior angles = 150*n Formula for sum of interior angles = 180*(n2)
180*(n2) = 150*n 30*n = 360
n = 360/30 = 12
Answer is D How did you get that step, I'm really bad at geometry... We are given y = 5x in the question statement. The two angles are supplementary (the two different angles made by the same line with another line) and hence add up to 180.
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Manager
Joined: 04 Oct 2011
Posts: 211
Location: India
Concentration: Entrepreneurship, International Business
GPA: 3

Re: The logo of a corporation [#permalink]
Show Tags
09 Jan 2013, 20:33
1
This post was BOOKMARKED
MacFauz wrote: From figure.,
x + y = 180 6*x = 180 x = 30, y = 150
Let number of sides be "n", hence number of interior angles is also "n" Sum of all interior angles = 150*n Formula for sum of interior angles = 180*(n2)
180*(n2) = 150*n 30*n = 360
n = 360/30 = 12
Answer is D hi MacFauz, x + y = 180 6*x = 180 x = 30, y = 150 i did this way 360/30 = 12 (since all angels are equal) I guess this will not work out in all cases ! Also how u figured out this ? Sum of all interior angles = 150*n
_________________
GMAT  Practice, Patience, Persistence Kudos if u like



VP
Joined: 02 Jul 2012
Posts: 1209
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: The logo of a corporation [#permalink]
Show Tags
09 Jan 2013, 21:29
1
This post received KUDOS
1
This post was BOOKMARKED
shanmugamgsn wrote: MacFauz wrote: From figure.,
x + y = 180 6*x = 180 x = 30, y = 150
Let number of sides be "n", hence number of interior angles is also "n" Sum of all interior angles = 150*n Formula for sum of interior angles = 180*(n2)
180*(n2) = 150*n 30*n = 360
n = 360/30 = 12
Answer is D hi MacFauz, x + y = 180 6*x = 180 x = 30, y = 150 i did this way 360/30 = 12 (since all angels are equal) I guess this will not work out in all cases ! Also how u figured out this ? Sum of all interior angles = 150*n There are "n" sides and since the figure is a polygon, there are "n" angles. Each interior angle is 150. So sum of all interior angles is 150 added "n" times or 150*n
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Senior Manager
Joined: 22 Nov 2010
Posts: 278
Location: India
WE: Consulting (Telecommunications)

Re: The logo of a certain corporation is in the shape of a polyg [#permalink]
Show Tags
18 Feb 2013, 05:22
fozzzy wrote: The logo of a certain corporation is in the shape of a polygon, where all angles of a the polygon have equal measures. In the above figure V is one vertex of the polygon. If Y in degrees is the measure of an angle of the polygon and y=5x how many sides does the polygon have?
A 5 B 6 C 10 D 12 E 30 x+y = 180 (straight line) x+5x= 180. x=30. Interior angle of polygon = 30 x 5 = 150. Interior Angle of regular polygon with side n no. of sides = (2n 4) * 90 / n 150 = (2n 4) * 90 / n. Solve it. n = 12.
_________________
YOU CAN, IF YOU THINK YOU CAN



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 624

Re: The logo of a corporation [#permalink]
Show Tags
21 Feb 2013, 06:55
shanmugamgsn wrote: MacFauz wrote: From figure.,
x + y = 180 6*x = 180 x = 30, y = 150
Let number of sides be "n", hence number of interior angles is also "n" Sum of all interior angles = 150*n Formula for sum of interior angles = 180*(n2)
180*(n2) = 150*n 30*n = 360
n = 360/30 = 12
Answer is D hi MacFauz, x + y = 180 6*x = 180 x = 30, y = 150 i did this way 360/30 = 12 (since all angels are equal) I guess this will not work out in all cases ! Basically what you have done(in red) is actually true for all regular polygons. We have the exterior angle as 30 degrees from the problem.Also, the sum of all the exterior angles in case of any polygon(regular/not regular) is always 360 degrees. As it is mentioned that this is a regualr polygon, only because of that, you can divide and get the answer as 12. Thus using the formula (n2)*180 is not necessary, atleast in this problem.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



VP
Joined: 02 Jul 2012
Posts: 1209
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: The logo of a corporation [#permalink]
Show Tags
21 Feb 2013, 07:50
vinaymimani wrote: shanmugamgsn wrote: MacFauz wrote: From figure.,
x + y = 180 6*x = 180 x = 30, y = 150
Let number of sides be "n", hence number of interior angles is also "n" Sum of all interior angles = 150*n Formula for sum of interior angles = 180*(n2)
180*(n2) = 150*n 30*n = 360
n = 360/30 = 12
Answer is D hi MacFauz, x + y = 180 6*x = 180 x = 30, y = 150 i did this way 360/30 = 12 (since all angels are equal) I guess this will not work out in all cases ! Basically what you have done(in red) is actually true for all regular polygons. We have the exterior angle as 30 degrees from the problem.Also, the sum of all the exterior angles in case of any polygon(regular/not regular) is always 360 degrees. As it is mentioned that this is a regualr polygon, only because of that, you can divide and get the answer as 12. Thus using the formula (n2)*180 is not necessary, atleast in this problem. Hi vinaymimani., That was actually shanmugamgsn's solution.. Great if it is correct.. But I would have needed to used the (n2)*180 formula since I did not know that sum of all exterior angles of a polygon is 360.. I have not heard of that before... Can you please illustrate the same in cases of a rectangle and triangle?
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 624

Re: The logo of a corporation [#permalink]
Show Tags
21 Feb 2013, 07:59
1
This post received KUDOS
Quote: Hi vinaymimani.,
That was actually shanmugamgsn's solution.. Great if it is correct.. But I would have needed to used the (n2)*180 formula since I did not know that sum of all exterior angles of a polygon is 360.. I have not heard of that before... Can you please illustrate the same in cases of a rectangle and triangle? Incase of a rectangle, the external angle for each side is (18090)degrees = 90 degrees. And there are 4 such angles. Thus the total sum of the external angles is 90*4 = 360 degrees. Incase of a triangle, let the 3 angles be a,b,c. a+b+c = 180 degrees.Now, the respective exterior angles are : 180a, 180b,180c. Thus, their sum is 180*3(a+b+c) = 180*2 = 360 degrees. I hope it's clear now. Once again, we can only divide 360 degrees by 30 degrees in this problem only because it is a regular polygon.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Manager
Joined: 07 May 2013
Posts: 104

Re: The logo of a certain corporation is in the shape of a polyg [#permalink]
Show Tags
17 Nov 2013, 18:11
Very simple. \(y=(n2)180/n\). \(x=180[(n2)180/n]\). Given y=5x. Substitute and solve for n.



Manager
Joined: 07 May 2013
Posts: 104

Re: The logo of a certain corporation is in the shape of a polyg [#permalink]
Show Tags
17 Nov 2013, 18:14
Hint: After equating 180 is cancelled throughout the equation. This makes calculations very easy.



Manager
Joined: 12 Jan 2013
Posts: 212

Re: The logo of a corporation [#permalink]
Show Tags
15 Dec 2013, 06:41
MacFauz wrote: Formula for sum of interior angles = 180*(n2)
Why does this apply? Why n2? I understand that the degrees of x + y = 180, but what relevance does that have in regards to the above 180*(n2)? I don't understand.



VP
Joined: 02 Jul 2012
Posts: 1209
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: The logo of a certain corporation is in the shape of a polyg [#permalink]
Show Tags
15 Dec 2013, 17:36
1
This post received KUDOS
For a polygon with 'n' sides, the sum of the interior angles is 180*(n2) For example, a triangle has 3 sides. So the sum of the interior angles is 180*(32) = 180 Sent from my iPhone using Tapatalk
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Manager
Joined: 13 Jul 2013
Posts: 69

Re: The logo of a corporation [#permalink]
Show Tags
05 Jan 2014, 23:54
MacFauz wrote: From figure.,
x + y = 180 6*x = 180 x = 30, y = 150
Let number of sides be "n", hence number of interior angles is also "n" Sum of all interior angles = 150*n Formula for sum of interior angles = 180*(n2)
180*(n2) = 150*n 30*n = 360
n = 360/30 = 12
Answer is D Can you tell me why Sum of all interior angles = 150*n? Are all the angles equal?



VP
Joined: 02 Jul 2012
Posts: 1209
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: The logo of a certain corporation is in the shape of a polyg [#permalink]
Show Tags
06 Jan 2014, 01:47
2
This post received KUDOS
Hi thegame001., The question states that all the angles of the polygon are equal. Since there are n sides and hence 'n' angles, the sum of all the angles is 150 added 'n' times and that is 150n. Sent from my iPhone using Tapatalk
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Current Student
Joined: 26 Jan 2013
Posts: 21

The logo of a certain corporation is in the shape of a polyg [#permalink]
Show Tags
23 Aug 2015, 01:51
1
This post received KUDOS
Here's a quicker way.
y + x = 180 y = 5x Hence, x = 30
Exterior angle, x = 360/n (since all angles are equal) n= 360/30 n = 12
Hope this helps.



Intern
Joined: 01 May 2017
Posts: 9

Re: The logo of a certain corporation is in the shape of a polyg [#permalink]
Show Tags
18 Nov 2017, 07:49
1
This post received KUDOS
While I would like to stay away from high level math and formulas, it helps to remember few formulas in case of Geometry questions. There are two pertinent flavors of the same formula that one should remember: 1  sum of interior angles of a polygon with n sides = 180 * (n  2) 2  Measure of each angle of a regular polygon* = \(\frac{[180 * (n  2) ]}{n}\)
A regular polygon* is a polygon that is equiangular* (all angles are equal in measure) and equilateral* (all sides have the same length) * https://en.wikipedia.org/wiki/Regular_polygonSo in this question, we have 2 simultaneous equations: y + x = 180 y  5x = 0 Solving these equations we get, y = 150 Using #2 150 = \(\frac{[180 * (n  2) ]}{n}\)[/color] Solving this we get n = 12



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11292
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: The logo of a certain corporation is in the shape of a polyg [#permalink]
Show Tags
12 Jan 2018, 14:33
Hi All, One of the rarer rules that can appear on the GMAT is "add a side, add 180 degrees" For example A triangle = 180 degrees A 4sided shape = 360 degrees A 5sided shape = 540 degrees A 6sided shape = 720 degrees Etc. In this prompt, we can use a combination of Geometry rules and the Answer choices to TEST THE ANSWERS. To start, we have to figure out the values of X and Y. Since those two angles form a line (thus, X+Y = 180) and Y = 5X, then X+5X = 180.... X=30 and Y=150 We're told that each of the angles in this unknown polygon is the SAME. We're asked for the number of sides that this polygon has. Using the above math rule, and the answer choices, we can work our way through the list until we find the polygon with equal 150 degree angles. Let's start with Answer B... Answer B: 6sided A 6sided shape = 720 degrees 720/(6 sides) = 120 degrees per side This is TOO SMALL (it's supposed to be 150 degrees), so we clearly need more sides/more degrees. Answer D: 12sided A 12sided shape = 180 + 9(180) = (10)180 = 1800 degrees 1800/(12 sides) = 150 degrees per side This is an exact MATCH for what we were told, so this must be the answer. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************




Re: The logo of a certain corporation is in the shape of a polyg
[#permalink]
12 Jan 2018, 14:33






