 It is currently 28 Sep 2020, 03:51 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Each of the triangles is equilateral.  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Active Member  Joined: 07 Jan 2018
Posts: 694
Followers: 11

Kudos [?]: 770 , given: 88

Each of the triangles is equilateral. [#permalink] 00:00

Question Stats: 40% (00:49) correct 59% (01:29) wrong based on 27 sessions
Attachment: 398-2.jpg [ 27.88 KiB | Viewed 1143 times ]

Each of the triangles is equilateral.

 Quantity A Quantity B The area of theshaded region $$6\pi$$

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.
[Reveal] Spoiler: OA VP Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1312  , given: 251

Re: Each of the triangles is equilateral. [#permalink]
1
KUDOS
amorphous wrote:
Each of the triangles is equilateral.

 Quantity A Quantity B The area of theshaded region 6π

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.

Given the radius of the circle is 3 (since one side of the equilateral triangle is 3)

Now the area of the circle =$$\pi * radius^2 = \pi * 3^2 = 9\pi$$

Now we need to find the area of the sector covered by the 2 equilateral triangle,

$$\frac{{Sector Area}}{{circle area}} = \frac{{Central angle}}{360}$$

Sector area =$$\frac{60}{360} * circle area =\frac{60}{360} * 9\pi = \frac{{3\pi}}{2}$$

Since there are two sectors so the total sectors not covered in shaded area =$$\frac{{6\pi}}{2}$$

Therefore the area under the shaded area = circle area - area of the 2 sectors = $$9\pi - \frac{{6\pi}}{2}= \frac{{12\pi}}{2} = 6\pi$$

Hence both are equal, i.e. option C
_________________

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

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Director Joined: 09 Nov 2018
Posts: 505
Followers: 0

Kudos [?]: 56 , given: 1

Re: Each of the triangles is equilateral. [#permalink]
pranab01 wrote:
amorphous wrote:
Each of the triangles is equilateral.

 Quantity A Quantity B The area of theshaded region 6π

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.

Given the radius of the circle is 3 (since one side of the equilateral triangle is 3)

Now the area of the circle =$$\pi * radius^2 = \pi * 3^2 = 9\pi$$

Now we need to find the area of the sector covered by the 2 equilateral triangle,

$$\frac{{Sector Area}}{{circle area}} = \frac{{Central angle}}{360}$$

Sector area =$$\frac{60}{360} * circle area =\frac{60}{360} * 9\pi = \frac{{3\pi}}{2}$$

Since there are two sectors so the total sectors not covered in shaded area =$$\frac{{6\pi}}{2}$$

Therefore the area under the shaded area = circle area - area of the 2 sectors = $$9\pi - \frac{{6\pi}}{2}= \frac{{12\pi}}{2} = 6\pi$$

Hence both are equal, i.e. option C

Sometime, in circle question, I have one problem. In this question, it doesn't say 'O' is the center. How would you confirm that answer is not D and calculate by confirming that 'O' is the center of the circle. Re: Each of the triangles is equilateral.   [#permalink] 18 Nov 2018, 15:52
Display posts from previous: Sort by

# Each of the triangles is equilateral.  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.