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

 It is currently 18 Oct 2019, 21:43

### 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

# On circle O, points C and D are on the same side of diameter AB, angle

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58453
On circle O, points C and D are on the same side of diameter AB, angle  [#permalink]

### Show Tags

27 Mar 2019, 20:39
00:00

Difficulty:

5% (low)

Question Stats:

100% (02:11) correct 0% (00:00) wrong based on 21 sessions

### HideShow timer Statistics

On circle O, points C and D are on the same side of diameter AB, angle AOC = 30°, and angle DOB = 45°. What is the ratio of the area of the smaller sector COD to the area of the circle?

(A) 2/9
(B) 1/4
(C) 5/18
(D) 7/24
(E) 3/10

Attachment:

6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png [ 10.64 KiB | Viewed 357 times ]

_________________
Director
Joined: 06 Jan 2015
Posts: 689
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: On circle O, points C and D are on the same side of diameter AB, angle  [#permalink]

### Show Tags

27 Mar 2019, 20:54
Bunuel wrote:

On circle O, points C and D are on the same side of diameter AB, angle AOC = 30°, and angle DOB = 45°. What is the ratio of the area of the smaller sector COD to the area of the circle?

(A) 2/9
(B) 1/4
(C) 5/18
(D) 7/24
(E) 3/10

Attachment:
6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png

The area of the smaller sector = pir^2((angle between the chord)/360)

Angle COD = 180 - 75 = 105

the ratio of the area of the smaller sector COD to the area of the circle = pir^2((angle between the chord)/360)/pir^2 ==> 105/360 ==> 7/24

Hence D
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Senior Manager
Joined: 13 Jan 2018
Posts: 342
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE: Consulting (Consulting)
Re: On circle O, points C and D are on the same side of diameter AB, angle  [#permalink]

### Show Tags

27 Mar 2019, 20:54
$$\angle COD = 105^{\circ}$$

Area of sector COD = $$\frac{\angle COD}{360^{\circ}}*\pi*r^2$$ ; where r is the radius of the circle.
Area of circle = $$\pi*r^2$$

$$\frac{Area of sector}{Area of circle}$$ = $$\frac{\frac{\angle COD}{360^{\circ}}*\pi*r^2}{\pi*r^2}$$

=$$\frac{105^{\circ}}{360^{\circ}}$$

= $$\frac{7}{24}$$

OPTION: D
_________________
____________________________
Regards,

Chaitanya

+1 Kudos

if you like my explanation!!!
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5020
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: On circle O, points C and D are on the same side of diameter AB, angle  [#permalink]

### Show Tags

28 Mar 2019, 02:23
Bunuel wrote:

On circle O, points C and D are on the same side of diameter AB, angle AOC = 30°, and angle DOB = 45°. What is the ratio of the area of the smaller sector COD to the area of the circle?

(A) 2/9
(B) 1/4
(C) 5/18
(D) 7/24
(E) 3/10

Attachment:
6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png

√COD = 105
and let radius of circle = 2 ; area = 4*pi
so
area of sector COD= 105/360 * 4*pi = 105/90 *pi
ratio
105/90 * pi / 4*pi
IMO D 7/24
Re: On circle O, points C and D are on the same side of diameter AB, angle   [#permalink] 28 Mar 2019, 02:23
Display posts from previous: Sort by