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 500,000 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]

Show Tags

01 Jul 2014, 05:17

Attachment:

star-sol.png [ 10.08 KiB | Viewed 2272 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]

Show Tags

19 Nov 2014, 09:54

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!
_________________

Cheers!!

JA If you like my post, let me know. Give me a kudos!

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

Show Tags

19 Nov 2014, 11:21

3

This post received KUDOS

1

This post was BOOKMARKED

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]

Show Tags

15 Dec 2014, 23:57

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]

Show Tags

27 Aug 2015, 18:08

1

This post received KUDOS

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)

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

Show Tags

16 Mar 2016, 07:48

Alternate Solution with just the basics. (I have not named every vertex separately in order to avoid confusion (mess). Every vertex of the star is named by the angle it depicts in the picture)

Attachments

File comment: y+A+B+C = 360 (sum of all the angles in quadrilateral-YABC ) A= 180-(y+v) (sum of all angles in a triangle is 180,Triangle YAV) B= 180-(x+z) (Triangle XBZ) C= 180-(y+w) (Triangle YCW)

Now, Substitute the values of A, B and C in the equation : A+B+C+y=360 (180-y-v) + (180-x-z) + (180-y-w) + y =360 By solving the above, we get: 540 - w - v - z - x - 2y + y=360 x+y+v+z+w=180 ANSWER - C

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

Show Tags

05 Nov 2016, 15:29

I think the easiest way to approach this problem was assuming we were dealing with a regular pentagon (all angles equal) and figuring out what each angle was using the interior angle formula --> (5-1)(180) = 540 --> 540/# of angles = 108

We know that the angle outside, opposite the interior angle of the pentagon is the same, therefore the two adjacent triangle angles will be 360-216 = 144. Divide by 2 to get them symmetrical and you will find each triangle off the pentagon has two angles that are 72 degrees, making the third of each 36.

In the figure shown, what is the value of v+x+y+z+w?

(A) 45 (B) 90 (C) 180 (D) 270 (E) 360

First, let's consider a PERFECT star.

Notice that the pentagon in the center is a perfect (regular) pentagon, which means ALL 5 angles are equal. The sum of the angles in an n-sided figure = 180(n-2) degrees So, the sum of the angles in this 5-sided figure = 180(5-2) = 180(3) = 540 degrees Since ALL 5 angles are equal, then the measure of each angle = 540/5 = 108 degrees.

Since two angles on a line must add to 180 degrees, we can see that the angles adjacent to the 108-degree angles must equal 72 degrees (since 180 - 108 = 72)

At this point, we can see that we're dealing with 5 triangles, and for each triangle, we know two of the angle measurements. Since the sum of the angles in a triangle = 180, we know that each missing angle = 36 degrees (180 - 72 - 72 = 36)

So, v + x + y + z + w = 36 + 36 + 36 + 36 + 36 = 180 degrees

In the figure shown, what is the value of v+x+y+z+w? [#permalink]

Show Tags

30 Jul 2017, 04:44

Although GMAT pictures may be not completely accurate and drawn to scale, I realize they don't usually try to "trick" users... Therefore I just drew the figure on a piece of paper and given the answer choices I realized the sum of the angles must be somewhere around 180 degrees:

Attachment:

star.png [ 31.16 KiB | Viewed 491 times ]

Probably this approach is not the most scientific and reliable way to solve the problem, but I guess it worked on this one.