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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach Starts Oct 17
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Chris Peckover, 100th-Percentile GMAT Scorer

Oct 17 · Chris Peckover
Sat · 11:00 AM to 2:00 PM ET
Oct 20 · Chris Peckover
Tue, Thu · 8:00 to 10:00 PM ET
Oct 25 · Josh Braslow
Sun · 1:00 to 4:00 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemand 5 seats left Start anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

PS 3

Expert replies
Source: — Problem Solving |

by parallel_chase » Wed Dec 24, 2008 6:31 am
the question is basically saying that a triangle is inscribed in a circle

circumference of the circle = 2*pi*r = 4 sqrt [(pi*sqrt3)]

pi * r = 2 sqrt [(pi*sqrt3)]

(pi*r)/2 = sqrt [(pi*sqrt3)]

[(pi*r)/2]^2 = (pi*sqrt3)

pi^2 * r^2/ 4 = pi * sqrt 3

pi * r^2/4 = sqrt 3

pi * r^2 = 4 * sqrt3 ---------I

probability of sand falling outside the triangle = 3/4

this means

area of the circle excluding the triangle / total area of the circle = 3/4

Therefore,

area of the triangle/ total area of the circle = 1-3/4 = 1/4------II


area of the circle = pi * r^2 = 4 * sqrt 3 [refer I]

area of the quilateral triangle = side^2 sqrt3/4

side^2 sqrt3/4 / 4 * sqrt 3 = 1/4 ---refer II


side^2 / 16 = 1/4

side^2 = 16/4

side^2 = 4

side = 2

Hence E.

This was an awesome question, took me about 3 mins to solve, but nonetheless brilliant.
No rest for the Wicked....
Join the discussion

Re: PS 3

by lunarpower » Thu Dec 25, 2008 1:12 am
the above post pretty much covers all the bases, but the lack of square root symbols makes it pretty hard to read.

HINT: google "square root symbol", copy one off one of the pages that appears (or even from the search results - you don't even have to click the links if the √ symbol appears in the first couple of lines of text), and then paste to your heart's delight.

you'll even save yourself work this way, because instead of typing "sqrt" (4 keystrokes), you can just hit ctrl-V (1 keystroke, or 2, depending on how you look at it) to paste the symbol.

i would've done the same for pi, but the pi character shows up as something very much resembling an 'n' on these forums.

--

if that's the circumference, then the radius is this quantity divided by 2p. (here 'p' stands for pi)
which is
(4√(P√3)) / 2P
= 2√(P√3)) / P **
= 2√√3 / √P *** - if you don't understand this step, i'll also show the work starting from (**).

starting from (***):
circle area = P(r^2)
= P * 4√3/P
= 4√3
so triangle area = 1/4 of this = √3

starting from (**):
circle area = P(r^2)
= P * 4P√3 / P^2
= 4√3
so triangle area = 1/4 of this = √3
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron
Join the discussion

by orel » Thu Dec 25, 2008 6:18 am
hi,
is it a GMAT type of question?
Join the discussion