GRE Official Guide Question Directory

It is currently 23 Apr 2021, 06:58

GRE Prep Club Tests

Decision Tracker

My Rewards

New comers' posts

New posts

Unanswered

GRE Prep 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 GRE 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.

Go to My Error Log Learn more

Request Expert Reply

Confirm Cancel

Apr 23
Get Your Game On: Preparing for Your Grad School Application [Free Guide]
08:00 PM PDT
-
09:00 PM PDT
Learn how to evaluate your profile, skills, and experiences to determine if, when, and where you should apply to graduate school.
Apr 28
Ignite Your GRE® Quant Score
08:00 PM PDT
-
10:00 PM PDT
A Revolutionary On-Demand GRE Prep Course with Target Test Prep. Try for $1

PREVIOUS TOPIC

NEXT TOPIC

Three circles with their centers on line segment PQ are tang

Tags :

Find Similar Topics About

Show Tags

Hide Tags

Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 15667

GRE 1: Q160 V160

Three circles with their centers on line segment PQ are tang [#permalink]

24 Feb 2017, 02:34

Expert Reply

00:00

Question Stats:

77% (00:57) correct

22% (00:57) wrong

based on 211 sessions

Hide Show timer Statistics

This question is a part of PowerPrep Question Collection

Attachment:

#GREpracticequestion Three circles with their centers on line segment PQ.jpg [ 12.07 KiB | Viewed 25967 times ]

Three circles with their centers on line segment PQ are tangent at points P, R, and Q, where point R lies on line segment PQ

Quantity A	Quantity B
The circumference of the largest circle	The sum of the circumferences of the two smaller circles

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Show Answer

Official Answer

Official Answer and Stats are available only to registered users. Register/Login.

_________________

GRE Prep Club OFFICIAL Android App

New to the GRE, and GRE CLUB Forum?
GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ
Search GRE Specific Questions | Download Vault
Posting Rules: QUANTITATIVE | VERBAL
FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)
Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests
GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection
Books: All GRE Best Books
Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)
How is the GRE Score Calculated -The Definitive Guide (2021)
Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)
Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Signature Read More

sandy

Retired Moderator

Joined: 07 Jun 2014

Posts: 4804

GRE 1: Q167 V156

WE:Business Development (Energy and Utilities)

Re: Three circles with their centers on line segment PQ are tang [#permalink]

28 Feb 2017, 16:40

Expert Reply

Explanation

We know that circumference of a circle = $\pi \times d$. Here D is diameter of circle.

One smaller circle has diameter PR and other is QR.

Diameter of the largest circle is PQ. Now PQR lie on the same line.

PR + QR = PQ

multiplying $\pi$ both side

$\pi \times PR + \pi \times QR = \pi \times PQ$.

Circumference of smaller circle with diameter PR + Circumference of smaller circle with diameter QR = Circumference of larger circle with diameter PQ.

Quantity B = Quantity A.

Hence C is correct option.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Signature Read More

Emike56

Intern

Joined: 08 Apr 2018

Posts: 44

Re: Three circles with their centers on line segment PQ are tang [#permalink]

15 Jun 2018, 03:49

sandy wrote:

Even though your explanation is still not clear, I will trust your reasoning on this one. Anytime I see a similar question, even if it has 5 circles inside the major circle and they are tangent, I will assume the circumference is equal to that of the major circle.

IshanGre

Manager

Joined: 29 Nov 2017

Posts: 190

Location: United States

GRE 1: Q142 V146

WE:Information Technology (Computer Software)

Re: Three circles with their centers on line segment PQ are tang [#permalink]

29 Aug 2018, 02:38

sandy wrote:

Explanation

We know that circumference of a circle = $\pi \times d$. Here D is diameter of circle.

One smaller circle has diameter PR and other is QR.

Diameter of the largest circle is PQ. Now PQR lie on the same line.

PR + QR = PQ

multiplying $\pi$ both side

$\pi \times PR + \pi \times QR = \pi \times PQ$.

Circumference of smaller circle with diameter PR + Circumference of smaller circle with diameter QR = Circumference of larger circle with diameter PQ.

"it is said in the question that R lies on a segment", I dont think it is safe to assume that the line segment shown and described in the circle is a diameter. in which case answer should be D...Please correct me if I am wrong.

Quantity B = Quantity A.

Hence C is correct option.

Director

Joined: 09 Nov 2018

Posts: 505

Re: Three circles with their centers on line segment PQ are tang [#permalink]

18 Jan 2019, 19:13

They are equal as two smaller diameters are equal to large

Director

Joined: 09 Nov 2018

Posts: 505

Re: Three circles with their centers on line segment PQ are tang [#permalink]

18 Jan 2019, 19:21

Emike56 wrote:

sandy wrote:

Hence C is correct option.

Even in this case also ha ha ha

Attachment:

Circle.jpg [ 29.88 KiB | Viewed 25431 times ]

GREAlumni2019

Intern

Joined: 22 Aug 2019

Posts: 9

Re: Three circles with their centers on line segment PQ are tang [#permalink]

15 Sep 2019, 06:51

I might not have done this efficiently but I tried plugging in numbers

For example the total distance is 8 and the 2 circles are equal

Big circle Circumference = 2pi*4=8pi
Small Circles Circumference = 2pi(2) +2pi(2) = 8pi

Not Equal - one has a diameter of 6 and the other 2
Big Circle = 2pi*4 = 8pi
Small Circles = 2pi(3) + 2pi(1) = 8pi

C

GR3A

Manager

Joined: 02 Sep 2019

Posts: 124

Concentration: Finance

GRE 1: Q151 V148

GPA: 3.14

Re: Three circles with their centers on line segment PQ are tang [#permalink]

29 Jun 2020, 23:33

It is more clear now.
Since the two small circles share the diameter with the big one, they have equal circumference.

Thanks
_________________

A simple guy with a big dreams.

Signature Read More

pprakash786

Manager

Joined: 20 Jun 2019

Posts: 168

GRE 1: Q158 V162

Re: Three circles with their centers on line segment PQ are tang [#permalink]

23 Jul 2020, 05:01

Emike56 wrote:

sandy wrote:

Fair bit of advice. Never assume anything unless it's given. I learned that the hard way.

Moreover, it's stated here that 'three circles with their centers on line segment PQ are tangent at points P, R, and Q where point R lies on segment PQ.' If centers are lying on PQ then we can say PQ is diameter of the biggest circle and thus solve as given.