The probability of the grain of sand landing on the portion of the base outside the triangle is 3/4. Hence, The probability of the grain of sand landing on the portion of the base inside the triangle is (1 - 3/4) = 1/4.
Therefore, the ratio of area of the triangle to the area of the base of the cylinder = 1/4
Say, length of each side of the equilateral triangle is a.
Hence, area of the equilateral triangle = (√3/4)*a²
Now, circumference of the base = 4√(π√3)
So, the radius of the base = 4√(π√3)/(2π)
So, area of the base = π[4√(π√3)/(2π)]² = π[16*(π√3)/(4π²)] = 4√3
Hence, area of the equilateral triangle = √3
Hence, (√3/4)*a² = √3 ---> a = √4 = 2
The correct answer is E.
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
Cylindrical tank
Source: Beat The GMAT — Problem Solving |
GMAT/MBA Expert
-
Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Location: Milpitas, CA
- Thanked: 1854 times
- GMAT Score:770
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
This problem feels to be very difficult but if read patiently then it is very easy. Here is what I did:
Given circumference 4√[�√3]
we know 2�r = 4√[�√3]
=> r = 2√[(√3)/�]
so Area of the base = �r^2 => � * (4√3)/�
Area of the base = 4√3
the problem says that the sand grain has a probability of falling outside the EQUILATERAL triangle is 3/4.
This means the area of the triangle is 1/4 of the total area of the base.
so area of the equilateral triangle is √3
But we know the area of the equilateral triangle is (√3/4)a^2
so (√3/4)a^2 = √3
a^2 = 4
a = 2
Answer is E
Given circumference 4√[�√3]
we know 2�r = 4√[�√3]
=> r = 2√[(√3)/�]
so Area of the base = �r^2 => � * (4√3)/�
Area of the base = 4√3
the problem says that the sand grain has a probability of falling outside the EQUILATERAL triangle is 3/4.
This means the area of the triangle is 1/4 of the total area of the base.
so area of the equilateral triangle is √3
But we know the area of the equilateral triangle is (√3/4)a^2
so (√3/4)a^2 = √3
a^2 = 4
a = 2
Answer is E
