Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 15:12

### 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

# What is the circumference of the circle above with center O?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 174
What is the circumference of the circle above with center O?  [#permalink]

### Show Tags

26 Dec 2012, 04:59
12
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:15) correct 19% (01:33) wrong based on 948 sessions

### HideShow timer Statistics

Attachment:

Circle.png [ 10.62 KiB | Viewed 18828 times ]
What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is $$20 + 10\sqrt{2}$$.
(2) The length of arc XYZ is $$5\pi$$.
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 56304
Re: What is the circumference of the circle above with center O?  [#permalink]

### Show Tags

26 Dec 2012, 05:05
1
4

What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is $$20 + 10\sqrt{2}$$. Since <O=90 degrees and OX=OZ=r, then $$XZ=r\sqrt{2}$$. Thus we have that $$r+r+r\sqrt{2}=20 + 10\sqrt{2}$$ --> we can find r, thus we can find the circumference. Sufficient.

(2) The length of arc XYZ is $$5\pi$$. Again, since <O=90 degrees, then the length of arc XYZ is 1/4 of the circumference (360 degrees), thus the circumference = $$20\pi$$. Sufficient.

Answer: D.
_________________
##### General Discussion
Director
Joined: 29 Nov 2012
Posts: 731
Re: What is the circumference of the circle above with center O?  [#permalink]

### Show Tags

12 Jan 2013, 08:33
Bunuel wrote:

What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is $$20 + 10\sqrt{2}$$. Since <O=90 degrees and OX=OZ=r, then $$XZ=r\sqrt{2}$$. Thus we have that $$r+r+r\sqrt{2}=20 + 10\sqrt{2}$$ --> we can find r, thus we can find the circumference. Sufficient.

(2) The length of arc XYZ is $$5\pi$$. Again, since <O=90 degrees, then the length of arc XYZ is 1/4 of the circumference (360 degrees), thus the circumference = $$20\pi$$. Sufficient.

Answer: D.

Is there a formula for this explanation?
Math Expert
Joined: 02 Sep 2009
Posts: 56304
Re: What is the circumference of the circle above with center O?  [#permalink]

### Show Tags

13 Jan 2013, 03:29
fozzzy wrote:
Bunuel wrote:

What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is $$20 + 10\sqrt{2}$$. Since <O=90 degrees and OX=OZ=r, then $$XZ=r\sqrt{2}$$. Thus we have that $$r+r+r\sqrt{2}=20 + 10\sqrt{2}$$ --> we can find r, thus we can find the circumference. Sufficient.

(2) The length of arc XYZ is $$5\pi$$. Again, since <O=90 degrees, then the length of arc XYZ is 1/4 of the circumference (360 degrees), thus the circumference = $$20\pi$$. Sufficient.

Answer: D.

Is there a formula for this explanation?

Yes, check here: math-circles-87957.html (see Arc Length under Arcs and Sectors chapter)
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14590
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the circumference of the circle above with center O?  [#permalink]

### Show Tags

02 Jan 2015, 14:06
2
Hi All,

Even though this DS question is about Geometry rules, it involves a great Algebra shortcut that you'll see at least once on Test Day.

We're given a circle with an ISOSCELES right triangle within it (with the 3 vertices at the center of the circle and on the circumference), so we have a 45/45/90 right triangle. We're asked for the circumference of the circle.

Fact 1: The perimeter of triangle OXZ = 20 + 10\sqrt{2}

Since the triangle is a 45/45/90, we know the sides are A, A and A\sqrt{2}, thus...

A + A + A\sqrt{2} = 20 + 10\sqrt{2}

We have ONE VARIABLE and ONE equation, so we CAN solve it (and since there are no additional possible answers, re. due to exponents, absolute values, etc. - there will be JUST ONE ANSWER.)
Fact 1 is SUFFICIENT.

Fact 2: Arc XYZ = 5pi

Since this arc is based on a 90 degree angle, we CAN figure out what fraction of the circumference we're dealing with (it's 1/4, but that math is not necessary). In this way we have the SAME shortcut that we had in Fact 1: ONE VARIABLE and ONE equation, so we CAN solve it.
Fact 2 is SUFFICIENT.

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

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Manager Joined: 22 Nov 2016 Posts: 205 Location: United States Concentration: Leadership, Strategy GPA: 3.4 Re: What is the circumference of the circle above with center O? [#permalink] ### Show Tags 06 Jul 2017, 17:48 We need to find the value of $$2 \pi R$$ From the figure we can tell that OX=OZ = radius or R. Since these two sides are equal and the other angle is given as $$90^ {\circ}$$, triangle XOZ is an isosceles right triangle with sides $$x:x:x\sqrt{2}$$ Armed with this info, lets look at the statements: Statement 1: Perimeter = $$20+10\sqrt{2}$$ This straight away gives us the radius as 10..........................Sufficient Statement 2: Length of arc XYZ = $$5\pi$$ We know that Length of an arc = $$x^{\circ}$$ * Circumference/360 Therefore, $$5\pi$$ = 90 * 2 * $$\pi$$ * R/360 We can find the circumference..........................Sufficient Answer is D _________________ Kudosity killed the cat but your kudos can save it. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7612 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the circumference of the circle above with center O? [#permalink] ### Show Tags 07 Jul 2017, 22:39 Walkabout wrote: Attachment: Circle.png What is the circumference of the circle above with center O? (1) The perimeter of triangle OXZ is $$20 + 10\sqrt{2}$$. (2) The length of arc XYZ is $$5\pi$$. Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. By Variable Approach method, we can identify a circle with just 1 varable, which is a radius. Thus D is the answer most likely. Let $$r$$ be the radius of the above circle. Condition 1) $$2 \cdot r + r\sqrt{2} = r \cdot (2 + \sqrt{2} ) = 20 + 10\sqrt{2}$$ Thus $$r = 10$$. This condition is sufficient. Condition 2) The arc XYZ is $$\frac{1}{4} \cdot 2 \pi r = 5 \pi$$. Thus $$r = 10$$. This condition is also sufficient. Therefore D is the answer as expected. -> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Joined: 19 Oct 2015
Posts: 26
Re: What is the circumference of the circle above with center O?  [#permalink]

### Show Tags

07 Jul 2017, 22:48
Answer is D
1. Traingle is 45,45,90 degree triangle.
So two sides are same and length of radius is 10
Circumference of circle is 20pi
2. Is an arc is is known and angle subtending that arc is known than radius can be calculated.
So Both 1 and 2 are sufficient.

D

Sent from my A0001 using GMAT Club Forum mobile app
Non-Human User
Joined: 09 Sep 2013
Posts: 11720
Re: What is the circumference of the circle above with center O?  [#permalink]

### Show Tags

18 Jul 2018, 08:36
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.
_________________
Re: What is the circumference of the circle above with center O?   [#permalink] 18 Jul 2018, 08:36
Display posts from previous: Sort by

# What is the circumference of the circle above with center O?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne