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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: In the figure shown, what is the value of v+x+y+z+w? [#permalink]
02 Jun 2014, 08:35

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. _________________

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

I can suggest two solutions:

Solution A

We can compute the sum of the angles from the five triangles created on the sides of the pentagon ABCDE. In those triangles, we have five pairs of congruent angles (see them marked by colored arcs in the attached drawing). Those angles are external angles for the pentagon and their sum is \(360^o\). See at the end of the post the justification for the fact that in every convex polygon, the sum of the external angles is \(360^o\). Therefore, v + x + y + z + w = 5 ∙ 180 – 2 ∙ 360 = 900 – 720= 180.

Solution B

Since the question is a multiple choice one, we can assume that there is one correct answer and that that answer does not depend on the shape of the “star”. Assuming that the star can be inscribed in a circle, we can see that the requested sum of the angles is 360/2 = 180, because each angle is inscribed in the circle and the five corresponding arcs complete the circle. Remark: If one of the answers would have been “It cannot be determined” or something similar, than this argument wouldn’t work.

Correct answer: C

Sum of the external angles for a convex polygon:

We know that the sum of the interior angles in a convex polygon with n sides (n being a positive integer greater than 2) is given by the formula: (n – 2)∙180 = 180n – 360. Each external angle is 180 – the corresponding interior angle. Therefore, the total sum of the exterior angles is 180n – (n – 2) ∙ 180 = 180n – 180n + 360 = 360.

Note: Convex polygons have the property that each of their angles is less than 180. All the polygons dealt with on GMAT are convex (triangle, quadrilateral, pentagon, hexagon,...) or are made up of convex polygons. In this question, the figure of the star, without the sides of the small convex pentagon, is an example of a non-convex decagon: it has 10 sides, and 5 angles which are greater, and 5, which are smaller than 180.

I don't get the equation of solution A... can anyone shed some light?

In the figure shown, what is the value of v+x+y+z+w? [#permalink]
01 Jul 2014, 04:17

Attachment:

star-sol.png [ 10.08 KiB | Viewed 646 times ]

i didn't know the central angle theorem, and tried solving with a different way. sorry for my mad paint skills :D

here is my solution: 1. Draw a line via vertex of angle Y, parallel to the line between angles V and Z. In a picture the red coloured lines are parallel. 2. Draw a line via vertex of angle Y, parallel to the line between angles X and Z (violet coloured) 3. Draw a line via vertex of angle Y, parallel to the line between angles X and W (blue coloured)

The following can be concluded from the pic accoridng to thales theorem: a. angles between red and violet lines will be same (angle Z) b. angles between black and red lines will be same (angle V) c. angles between blue and black lines will be same (angle W) d. angles between blue and violet lines will be same (angle X)

as a result sum of 5 angles will be a violet line and equal to 180 degrees

My solution is obviously not as simple and quick as Bunuel's one, but maybe you can use my approach for solving similar problems

Re: In the figure shown, what is the value of v+x+y+z+w? [#permalink]
19 Nov 2014, 08:54

Bunuel wrote:

Let's simplify the problem by imagining that we have a star that is inscribed in a circle as shown below:

Hi Bunuel. How can we assume that the star could be inscribed within a circle in the absence of information. Further, the general GMAT assumption is that all diagrams are not drawn to scale unless the contrary is mentioned.

Am I missing anything here? Please help! _________________

Re: In the figure shown, what is the value of v+x+y+z+w? [#permalink]
19 Nov 2014, 10:21

1

This post received KUDOS

Wow! See what I found with a little googling!

A star is always regularly shaped (this clarifies why Bunuel assumed that the start would get inscribed in the circle)! 1. The sum of the angles formed at the tips of the five pointed star is 180; the sum of the angles formed at the tips of the six pointed star is 360. 2. The formula for the sum of the angle measurements at the tips of an n-pointed star is f(n)=180(n)-720 where n is an integer greater than 4.

Re: In the figure shown, what is the value of v+x+y+z+w? [#permalink]
15 Dec 2014, 22:57

Hi Bunuel, can you please elaborate how you made the assumption that "Let's simplify the problem by imagining that we have a star that is inscribed in a circle as shown below"?

Re: In the figure shown, what is the value of v+x+y+z+w? [#permalink]
15 Dec 2014, 22:57

Hi Bunuel, can you please elaborate how you made the assumption that "Let's simplify the problem by imagining that we have a star that is inscribed in a circle as shown below"?

Re: In the figure shown, what is the value of v+x+y+z+w? [#permalink]
27 Aug 2015, 17:08

Interior angle of a polygon = \(((n-2)180)/n\) For Pentagon = \((5-3)180/5\) = 108 sum of angles in each triangle angle x+(180-108)+(180-108) = 180 .... x = 36 there are 5 triangles ... 36*5 = 180 Answer (C)

gmatclubot

Re: In the figure shown, what is the value of v+x+y+z+w?
[#permalink]
27 Aug 2015, 17:08

Hey, everyone. After a hectic orientation and a weeklong course, Managing Groups and Teams, I have finally settled into the core curriculum for Fall 1, and have thus found...

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

After I was accepted to Oxford I had an amazing opportunity to visit and meet a few fellow admitted students. We sat through a mock lecture, toured the business...