GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jan 2019, 00:23

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# The points R, T, and U lie on a circle that has radius 4. If

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52274
The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

11 Mar 2014, 22:58
3
24
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:16) correct 30% (02:31) wrong based on 1050 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is $$\frac{4*\pi}{3}$$, what is the length of line segment RU?

(A) 4/3
(B) 8/3
(C) 3
(D) 4
(E) 6

Problem Solving
Question: 153
Category: Geometry Circles; Triangles; Circumference
Page: 82
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND 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:
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!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52274
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

11 Mar 2014, 22:59
1
8
SOLUTION

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is $$\frac{4*\pi}{3}$$, what is the length of line segment RU?

(A) 4/3
(B) 8/3
(C) 3
(D) 4
(E) 6

The circumference of a circle=$$2*\pi*r=8*\pi$$, $$\frac{RTU}{8*\pi}= \frac{(\frac{4*\pi}{3})}{8\pi}=\frac{1}{6}$$. --> Angle $$\angle{RCU}=\frac{360}{6}=60$$ degrees (C center of the circle).

RCU is isosceles triangle as $$RC=CU=r$$ and $$RCU=CRU=CUR=60$$ degrees. Hence $$RU=r=4$$.

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1823
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

Updated on: 07 May 2014, 01:08
13
6

Perimeter of Circle $$= 8 \pi$$

Perimeter of arc $$= 4 \frac{\pi}{3}$$

So, $$8 \pi * \frac{1}{6} = 4 \frac{\pi}{3}$$

means Perimeter of arc is $$\frac{1}{6}$$ th the Perimeter of Circle

So Angle ROU$$= \frac{360}{6} = 60$$ Deg

Triangle ROU was already an isosceles triangle (as inscribed in circle) with equal sides = 4

Now as its a equilateral triangle, RU = 4
Attachments

rt.jpg [ 14.41 KiB | Viewed 11582 times ]

_________________

Kindly press "+1 Kudos" to appreciate

Originally posted by PareshGmat on 12 Mar 2014, 19:28.
Last edited by PareshGmat on 07 May 2014, 01:08, edited 1 time in total.
##### General Discussion
Intern
Joined: 10 Apr 2008
Posts: 25
Location: India
GMAT 1: 560 Q39 V28
WE: Consulting (Computer Software)
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

25 Dec 2014, 01:45
I think the important point here is to understand the transition from isosceles triangle to equilateral. If you can quickly see that despite being isosceles, it is also equilateral triangle, you will be able to answer the Q. I missed this point and ended up marking wrong answer..
Manager
Joined: 26 Feb 2015
Posts: 115
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

09 Apr 2015, 05:58
So if the circumference of the circle is 8 (since radius 4). So 360 degrees is 8pi. (4pi/3)/8pi is 1/6. So RTU has at least one angle with 60 degrees, the other angles could be 30 + 90 or 60 + 60, or am I misintepreting the question?
Math Expert
Joined: 02 Sep 2009
Posts: 52274
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

09 Apr 2015, 06:08
erikvm wrote:
So if the circumference of the circle is 8 (since radius 4). So 360 degrees is 8pi. (4pi/3)/8pi is 1/6. So RTU has at least one angle with 60 degrees, the other angles could be 30 + 90 or 60 + 60, or am I misintepreting the question?

Check the image below:
Attachment:

Untitled.png [ 3.98 KiB | Viewed 9907 times ]

Angle RCU = 60°. $$RC=CU=r$$ and $$RCU=CRU=CUR=60$$ degrees. Hence $$RU=r=4$$.
_________________
Joined: 30 May 2015
Posts: 38
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

11 Feb 2017, 13:01
Let consider O as the centre of circle and r as radius
2πr * ((∠ROU)/360) = 4π/3
After solving it ∠ROU = 60
now OR = OU (Radius of the circle)
which means ∠ORU = ∠OUR = 60 (Opposite angles of two opposite sides will be equal and some of three angles of triangle is 180)
as all three angles are 60 degree, which means it is equilateral triangle.
So Answer => OR = OU = RU = 4
Manager
Joined: 21 Jun 2017
Posts: 83
The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

11 Oct 2017, 11:39
Given radius is 4, you immediately know that triangle ROU is an Isosceles. But, since we are not given the degrees, we do not know at first if the triangle is an equilateral.

Circumference of a circle = 2pi r = 8pi
arc = x/360(circumference)

4pi/3/8pi = x/360
480/8pi = 60 = x

So, with 60 degrees as our angle in triangle ROU, and with two sides equal, we can deduce that the two unknown angles is 60, 60, making the triangle ROU an equilateral triangle.

All sides are equal in an equilateral triangle, therefore, RU = 4, Answer (D)
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

16 Oct 2017, 15:55
Bunuel wrote:

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is $$\frac{4*\pi}{3}$$, what is the length of line segment RU?

(A) 4/3
(B) 8/3
(C) 3
(D) 4
(E) 6

We can let the center of the circle be C. Since the radius of circle C is 4, its circumference is 2πr = 2π4 = 8π.

We can use the following proportion to determine the central angle:

x/360 = (4π/3)/8π

x/360 = 4π/24π

x/360 = 1/6

x = 60

Now triangle RUC (i.e., the triangle formed by radii RC and UC and chord RU) is at least an isosceles triangle, since RC = UC = 4. However, since x = 60 degrees, or angle RCU = 60 degrees, triangle RUC must be equilateral because angles RUC and URC are also 60 degrees. Since triangle RUC is equilateral, RU = RC = 4.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 08 Aug 2017
Posts: 6
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

20 Oct 2017, 10:03
JeffTargetTestPrep wrote:
Bunuel wrote:

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is $$\frac{4*\pi}{3}$$, what is the length of line segment RU?

(A) 4/3
(B) 8/3
(C) 3
(D) 4
(E) 6

We can let the center of the circle be C. Since the radius of circle C is 4, its circumference is 2πr = 2π4 = 8π.

We can use the following proportion to determine the central angle:

x/360 = (4π/3)/8π

x/360 = 4π/24π

x/360 = 1/6

x = 60

Now triangle RUC (i.e., the triangle formed by radii RC and UC and chord RU) is at least an isosceles triangle, since RC = UC = 4. However, since x = 60 degrees, or angle RCU = 60 degrees, triangle RUC must be equilateral because angles RUC and URC are also 60 degrees. Since triangle RUC is equilateral, RU = RC = 4.

how do we know RC = UC?

Thanks
Retired Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 986
Location: India
GPA: 3.64
The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

20 Oct 2017, 10:15
Length of arc RTU=4π/3
Angle subtended at the centre=$$\frac{4π}{3}$$/(2π*4)*360 =60 deg.
In triangle RCU, radius, RC=CU=4, hence each angle is 60 deg and triangle is equilateral triangle.
Hence RU=4
_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 199
Location: India
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

19 Nov 2017, 00:51
Sorry this might seem like a silly question but why is a triangle formed here . I could find the degree measure of the and also find the length the circumference and am not understanding how to proceed further. Can someone suggest way to solve this question without assuming the triangle formed . thank you
Manager
Joined: 12 Nov 2016
Posts: 137
Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39
GMAT 2: 650 Q47 V33
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

21 Nov 2017, 09:11
Why make a life harder and resolve via a triangle?
I got another comment - in this type of questions it is likely that a triangle is equilateral otherwise it would be too difficult to find the line segment, right? Wouldn't it be safe to assume so?
VP
Joined: 09 Mar 2016
Posts: 1287
Re: The points R, T, and U lie on a circle that has radius 4. If  [#permalink]

### Show Tags

15 Apr 2018, 06:04
Bunuel wrote:
SOLUTION

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is $$\frac{4*\pi}{3}$$, what is the length of line segment RU?

(A) 4/3
(B) 8/3
(C) 3
(D) 4
(E) 6

The circumference of a circle=$$2*\pi*r=8*\pi$$, $$\frac{RTU}{8*\pi}= \frac{(\frac{4*\pi}{3})}{8\pi}=\frac{1}{6}$$. --> Angle $$\angle{RCU}=\frac{360}{6}=60$$ degrees (C center of the circle).

RCU is isosceles triangle as $$RC=CU=r$$ and $$RCU=CRU=CUR=60$$ degrees. Hence $$RU=r=4$$.

Bunuel hello

How do you visuilize in mind and understand that we talk about triangle let alone isolosces ? please explain:)
Re: The points R, T, and U lie on a circle that has radius 4. If &nbs [#permalink] 15 Apr 2018, 06:04
Display posts from previous: Sort by