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:

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.

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

Show Tags

25 Jun 2012, 02:52

18

This post received KUDOS

Expert's post

9

This post was BOOKMARKED

SOLUTION

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

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

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

As we can see, 5 arcs subtended by the inscribed angles (x, y, z, w, and v) make the whole circumference. Hence the sum of the corresponding central angles must be 360 degrees, which makes the sum of the inscribed angels 360/2=180 degrees (according to the Central Angle Theorem the measure of inscribed angle is always half the measure of the central angle).

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.

Attachments

OG13-D10-A.png [ 26.98 KiB | Viewed 24602 times ]

OG13-D10-B.png [ 38.38 KiB | Viewed 24269 times ]

_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

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

Show Tags

25 Jun 2012, 04:58

As shown in the diagrams above, nothing about the colored angles can be assumed. So I considered triangles that forms the interior angles of the inside pentagon. Sum of those individual angles = 360

Bases on the above method I am getting 270 as my answer

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

Show Tags

29 Jun 2012, 03:46

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

SOLUTION

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

Attachment:

Star.png [ 9.16 KiB | Viewed 26898 times ]

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

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

Attachment:

Star2.png [ 43.64 KiB | Viewed 27473 times ]

As we can see, 5 arcs subtended by the inscribed angles (x, y, z, w, and v) make the whole circumference. Hence the sum of the corresponding central angles must be 360 degrees, which makes the sum of the inscribed angels 360/2=180 degrees (according to the Central Angle Theorem the measure of inscribed angle is always half the measure of the central angle).

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

Show Tags

29 Jun 2012, 11:49

1

This post received KUDOS

The sum of all the angles of the pentagon in the middle is (5-3)180 = 540. Each vertex of the pentagon has a angle of 108 degrees (on average). Lets look at triangle AYW, since A is a vertex of the pentagon, the sum of y + w = 72. In this same scenario z + v also = 72 and x equals 36 (72/2).

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

Show Tags

29 Jun 2012, 14:50

ashish8 wrote:

The sum of all the angles of the pentagon in the middle is (5-3)180 = 540. Each vertex of the pentagon has a angle of 108 degrees (on average). Lets look at triangle AYW, since A is a vertex of the pentagon, the sum of y + w = 72. In this same scenario z + v also = 72 and x equals 36 (72/2).

Nice! In other words, if we understand from the answers that the sum does not depend on the shape of the star, we can consider a regular pentagon. Then each of its angles is 108, and each angle of the star is 36, so the sum is 180. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

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

Show Tags

25 Dec 2012, 04:48

Bunuel wrote:

fozzzy wrote:

Bunuel wrote:

SOLUTION

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

Attachment:

Star.png

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

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

Attachment:

Star2.png

As we can see, 5 arcs subtended by the inscribed angles (x, y, z, w, and v) make the whole circumference. Hence the sum of the corresponding central angles must be 360 degrees, which makes the sum of the inscribed angels 360/2=180 degrees (according to the Central Angle Theorem the measure of inscribed angle is always half the measure of the central angle).

Answer: C.

could you please elaborate on this method. very interesting approach.

You should tell what exactly didn't you understand.

the highlighted part.... have a difficult time to apply the theory properly. _________________

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/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

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

Show Tags

27 Dec 2012, 03:33

fozzzy wrote:

I was thinking of using the exterior angle property with 2 triangles

Angle 1 = X + W Angle 2 = v + Y

angle 1 + angle 2 + Z = 180

then add those angles up its 180 degrees.

Excellent fozzy..! KUDOS for providing fastest possible soln to this problem I believe as I also did in the same way but didn't post seeing the rest of the solns..Their knowledge base is so widened man than ours.. but still it's the fastest possible.. _________________

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

Show Tags

15 Jan 2013, 21:04

debayan222 wrote:

fozzzy wrote:

I was thinking of using the exterior angle property with 2 triangles

Angle 1 = X + W Angle 2 = v + Y

angle 1 + angle 2 + Z = 180

then add those angles up its 180 degrees.

Excellent fozzy..! KUDOS for providing fastest possible soln to this problem I believe as I also did in the same way but didn't post seeing the rest of the solns..Their knowledge base is so widened man than ours.. but still it's the fastest possible..

Thanks! Theory is really important in GMAT, bunuel's explanation is pretty fast if you know the theory _________________

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/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

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

Show Tags

28 Apr 2013, 08:21

Hi Bunuel,

I didn't understand the part where you used "Central Angle Theorem". Is it correct to assume that if I see one or more triangles then If I draw a circle around those triangles which are kind of inter-connected then can I use the "Central Angle Theorem"?

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

Show Tags

29 Apr 2013, 00:59

1

This post received KUDOS

Expert's post

nitestr wrote:

Hi Bunuel,

I didn't understand the part where you used "Central Angle Theorem". Is it correct to assume that if I see one or more triangles then If I draw a circle around those triangles which are kind of inter-connected then can I use the "Central Angle Theorem"?

Thanks a lot for the help,

LR

Not sure understand what you mean.

Anyway, the Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle:

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

Show Tags

29 Apr 2013, 08:57

I'm ok with the Theorem, but I want to know how you came up the assumption " Let's simplify the problem by imagining that we have a star that is inscribed in a circle as shown below" as you mentioned above?

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

Show Tags

24 May 2013, 01:48

1

This post received KUDOS

nitestr wrote:

I'm ok with the Theorem, but I want to know how you came up the assumption " Let's simplify the problem by imagining that we have a star that is inscribed in a circle as shown below" as you mentioned above?

You are right, not always can we conclude that five points in a plan are co-circular; while it is true that three points are always co-circular.

However, the solution works if we imagine two circles for three points each. It was just a coincidence that the assumption that all the given points are co-circular worked.

gmatclubot

Re: In the figure shown, what is the value of v+x+y+z+w?
[#permalink]
24 May 2013, 01:48

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

I barely remember taking decent rest in the last 60 hours. It’s been relentless with submissions, birthday celebration, exams, vacating the flat, meeting people before leaving and of...

Rishabh from Gyan one services, India had a one to one interview with me where I shared my experience at IMD till now. http://www.gyanone.com/blog/life-at-imd-interview-with-imd-mba/ ...