BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

In the figure above, equilateral triangle ABC is inscribed

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Sun May 19, 2019 9:28 am
By symmetry, since the triangle is equilateral, the length of each circular arc between two adjacent corners of the triangle must make up 1/3 of the entire circumference of the circle. Since the arc ABC is two of those arcs put together, 24 is 2/3 of the circumference, and 36 is the entire circumference. Since the circumference equals π*d, where d is the diameter, π*d = 36, and d = 36/π, and since π is slightly bigger than 3, d is slightly less than 12, and 11 is the only reasonable answer among the choices.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Tue May 21, 2019 6:28 pm
BTGmoderatorDC wrote:Image

In the figure above, equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?

A. 5
B. 8
C. 11
D. 15
E. 19

OA C

Source: GMAT Prep
We are given the length of arc ABC is equal to 24. Since arc AB, BC, and CA each represent 1/3 of the circumference, arc ABC represents 2/3 of the circumference. Thus, we can create the following equation.

2/3(circumference) = 24

2/3(Ï€d) = 24

Ï€d = 24 x 3/2

Ï€d = 36

d = 36/Ï€

d ≈ 11

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1