It is currently 21 Mar 2018, 02:19

### 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 June
Open Detailed Calendar

# PQ, QR and PR are diameters of the three circles shown above. If QR =

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44373
PQ, QR and PR are diameters of the three circles shown above. If QR = [#permalink]

### Show Tags

29 Nov 2017, 23:07
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:25) correct 29% (01:33) wrong based on 33 sessions

### HideShow timer Statistics

PQ, QR and PR are diameters of the three circles shown above. If QR = 4, and PQ = 2QR, what is the area of the shaded region?

(A) 6π
(B) 8π
(C) 10π
(D) 12π
(E) 16π

[Reveal] Spoiler:
Attachment:

2017-11-30_1001_002.png [ 8.33 KiB | Viewed 736 times ]
[Reveal] Spoiler: OA

_________________
Senior Manager
Joined: 17 Oct 2016
Posts: 327
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: PQ, QR and PR are diameters of the three circles shown above. If QR = [#permalink]

### Show Tags

29 Nov 2017, 23:23
D.

From question we can calculate PR=12 PQ=8.
Now shaded area= 0.5*(area of circle of dia PR-area of circle of dia PQ)+0.5*(area of circle of dia QR)
On solving this gives pi/8*(12^2-8^2+4^2)
= pi/8*(96)
=12pi

Sent from my iPhone using GMAT Club Forum
_________________

Help with kudos if u found the post useful. Thanks

VP
Joined: 22 May 2016
Posts: 1427
PQ, QR and PR are diameters of the three circles shown above. If QR = [#permalink]

### Show Tags

30 Nov 2017, 08:20
Bunuel wrote:

PQ, QR and PR are diameters of the three circles shown above. If QR = 4, and PQ = 2QR, what is the area of the shaded region?

(A) 6π
(B) 8π
(C) 10π
(D) 12π
(E) 16π

[Reveal] Spoiler:
Attachment:
The attachment 2017-11-30_1001_002.png is no longer available

Attachment:

eeeeee.png [ 13.05 KiB | Viewed 405 times ]

Find areas of circles, then divide by 2 (shaded and unshaded regions are in semicircles)
To find shaded area: Use just the bottom half + $$\frac{1}{2}$$ Circle QR

Circle QR diameter = 4, r = 2
Circle QR area = $$4\pi$$
$$\frac{1}{2} * 4\pi = 2\pi$$
= $$\frac{1}{2}$$ Area of Circle QR

Circle PQ diameter: (2*4) = 8, r = 4
Circle PQ area = $$16\pi$$
$$\frac{1}{2} * 16\pi = 8\pi$$
= $$\frac{1}{2}$$ Area of Circle PQ

Circle PR diameter: (4 + 8 = 12), r = 6
Circle PR area = $$36\pi$$
$$\frac{1}{2} * 36\pi = 18\pi$$
= $$\frac{1}{2}$$ Area of Circle PR

Shaded area = Use just the bottom half ($$\frac{1}{2}$$ PR + $$\frac{1}{2}$$ QR) - $$\frac{1}{2}$$PQ
$$\frac{1}{2}$$ QR is the little shaded area in the top half

Shaded area = Areas of
($$\frac{1}{2}$$ of shaded large Circle PR + $$\frac{1}{2}$$ shaded little Circle QR)* - $$\frac{1}{2}$$ unshaded medium Circle PQ
$$(18\pi + 2\pi) - 8\pi$$
$$20\pi - 8\pi = 12\pi$$

No need to account for the $$\frac{1}{2}$$ shaded little Circle QR in the bottom half; it is included in $$\frac{1}{2}$$ big Circle QR in the bottom half
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 878
Re: PQ, QR and PR are diameters of the three circles shown above. If QR = [#permalink]

### Show Tags

30 Nov 2017, 12:22
1
KUDOS
Expert's post
Bunuel wrote:

PQ, QR and PR are diameters of the three circles shown above. If QR = 4, and PQ = 2QR, what is the area of the shaded region?

(A) 6π
(B) 8π
(C) 10π
(D) 12π
(E) 16π

[Reveal] Spoiler:
Attachment:
2017-11-30_1001_002.png

We know that $$QR = 4$$.

Thus $$PQ = 2QR = 8$$ and $$PR = PQ + QR = 8 + 4 =12$$

The area of the shaded region = Area of semi-circle with diameter QR + Area of semi-circle with diameter PR - Area of semi-circle with diameter PQ

Area of shaded region
$$= \frac{π}{2}*(\frac{4}{2})^2 + \frac{π}{2}*(\frac{12}{2})^2 - \frac{π}{2}*(\frac{8}{2})^2$$

$$=2π + 18π - 8π$$

$$= 12π$$

The correct answer is Option D.
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2319
Location: United States (CA)
Re: PQ, QR and PR are diameters of the three circles shown above. If QR = [#permalink]

### Show Tags

03 Dec 2017, 18:38
1
KUDOS
Expert's post
Bunuel wrote:

PQ, QR and PR are diameters of the three circles shown above. If QR = 4, and PQ = 2QR, what is the area of the shaded region?

(A) 6π
(B) 8π
(C) 10π
(D) 12π
(E) 16π

[Reveal] Spoiler:
Attachment:
2017-11-30_1001_002.png

We are given that QR = 4 and PQ = 2QR; thus, PQ = 8. To determine the area of the shaded region, we can first determine the area of semicircle PR and then subtract the area of semicircle PQ from it. Then we add in the area of semicircle QR. Notice that radii of semicircles PR, PQ and QR are 6, 4 and 2, respectively.

Area of semicircle PR = 6^2 x π x 1/2 = 18π

Area of semicircle PQ = 4^2 x π x 1/2 = 8π

Area of semicircle QR = 2^2 x π x 1/2 = 2π

Thus, the area of the shaded region is 18π - 8π + 2π = 12π.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: PQ, QR and PR are diameters of the three circles shown above. If QR =   [#permalink] 03 Dec 2017, 18:38
Display posts from previous: Sort by

# PQ, QR and PR are diameters of the three circles shown above. If QR =

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.