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

 It is currently 21 Oct 2019, 13:23

### 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

# A circle of radius 2 is inscribed in a semicircle, as shown. The area

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58396
A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

### Show Tags

28 Mar 2019, 00:55
00:00

Difficulty:

15% (low)

Question Stats:

92% (01:39) correct 8% (04:51) wrong based on 26 sessions

### HideShow timer Statistics

A circle of radius 2 is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?

(A) 1/2

(B) $$\frac{\pi}{6}$$

(C) $$\frac{2}{\pi}$$

(D) 2/3

(E) $$\frac{3}{\pi}$$

Attachment:

b576665e4dd6ec10b3ec91bcda2f520bbd9d9846.png [ 10.71 KiB | Viewed 473 times ]

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58396
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

### Show Tags

28 Mar 2019, 00:58
Bunuel wrote:

A circle of radius 2 is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?

(A) 1/2

(B) $$\frac{\pi}{6}$$

(C) $$\frac{2}{\pi}$$

(D) 2/3

(E) $$\frac{3}{\pi}$$

Attachment:
b576665e4dd6ec10b3ec91bcda2f520bbd9d9846.png

Check other Shaded Region Problems in our Special Questions Directory.
_________________
Manager
Joined: 31 Dec 2018
Posts: 114
Location: India
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

### Show Tags

28 Mar 2019, 01:29
Ans= Area of smaller circle/Area of semi circle
A= π2²/π4²/2
A=2*2²/4²=1/2

OA=A

Posted from my mobile device
Senior Manager
Joined: 13 Feb 2018
Posts: 450
GMAT 1: 640 Q48 V28
A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

### Show Tags

28 Mar 2019, 01:37
mohitranjan05 wrote:
Ans= Area of smaller circle/Area of semi circle
A= π2²/π4²/2
A=2*2²/4²=1/2

OA=A

Posted from my mobile device

The stem asks: $$\frac{area of semi - area of circle}{area of semi}$$

you just got lucky that area of semi - area of circle = area of circle
Otherwise, you could go wrong

Regards
L
Senior Manager
Joined: 25 Feb 2019
Posts: 336
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

### Show Tags

28 Mar 2019, 02:05
1
IMO A.

area of semicircle = (π 4^2)/2
= 16π/2=8π

area of inscribed circle = π 2^2 = 4π

aonthe shaded area = 8π-4π =4π

which is half of semicircle

so in fraction it is 1/2

IMO A

Posted from my mobile device
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5027
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area  [#permalink]

### Show Tags

28 Mar 2019, 03:22
area of semicircle ; 8 pi and of circle = 4pi
so ratio
4pi/8pi = 1/2
IMO A

Bunuel wrote:

A circle of radius 2 is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?

(A) 1/2

(B) $$\frac{\pi}{6}$$

(C) $$\frac{2}{\pi}$$

(D) 2/3

(E) $$\frac{3}{\pi}$$

Attachment:
b576665e4dd6ec10b3ec91bcda2f520bbd9d9846.png
Re: A circle of radius 2 is inscribed in a semicircle, as shown. The area   [#permalink] 28 Mar 2019, 03:22
Display posts from previous: Sort by