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

Redeem
TTP OnDemand GMAT Video Course
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
Start Free 5-Day Trial Read 559 Reviews →

What is the greatest possible number of points

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 366
Joined: Fri Jun 05, 2015 3:35 amFollowed by: 2 members
Thanked: 3 times
by NandishSS » Tue Jul 18, 2017 7:52 am
What is the greatest possible number of points at which 11 circles with different radii intersected one another?

A. 45
B. 60
C. 85
D. 90
E. 110

OA: E

Source: Math Revolution
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 416
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

by regor60 » Tue Jul 18, 2017 9:00 am
NandishSS wrote:What is the greatest possible number of points at which 11 circles with different radii intersected one another?

A. 45
B. 60
C. 85
D. 90
E. 110

OA: E

Source: Math Revolution
Two circles can intersect at two points at the most.

How many different pairs of two circles can be generated from 11 ?

11!/2!9! = 55 unique pairs x 2 intersections/pair = E
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

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

by Ian Stewart » Tue Jul 18, 2017 8:47 pm
Same idea as the post above, but using more elementary principles: draw just one circle first. Then draw another - it can intersect the first at 2 points, at most. Then draw a third. It can intersect each of the first two circles at two points, so we can make 4 new intersection points. Similarly the next circle can create 6 new intersection points, and so on. So the maximum total number of intersection points will be

2 + 4 + 6 + ... + 18 + 20

which is an equally spaced sum with 10 terms. The average term in that sum is the average of the smallest and largest terms, so is 11, and since sum = avg*number of terms, the sum is thus 11*10 = 110.
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
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members
Location: Grand Central / New York
Thanked: 470 times

by Jay@ManhattanReview » Tue Jul 18, 2017 11:32 pm
NandishSS wrote:What is the greatest possible number of points at which 11 circles with different radii intersected one another?

A. 45
B. 60
C. 85
D. 90
E. 110

OA: E

Source: Math Revolution
Two circles with unequal radii can intersect each other at the most two points.

The first circle can intersect the other 10 circles in 2 x 10 = 20 points.

Thus 11 circles would intersect each other in (20/2)*11 = 110 points. We divided the number of points by '2' because the intersecting points were counted twice.

The correct answer: E

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1