start counting intersections from any corner and you will notice that they increase/decrease in raw 1:3:5:7:9:7:5:3:1. Sum them up to get precisely 41 intersections for 4x4 square. For square 5x5 not shown here and outside of this question's picture (imaginery) this will be 1:3:5:7:9:11:9:7:5:3:1, by summing up we get 61
d
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
geometry
Source: Beat The GMAT — Problem Solving |
-
tomada
- Master | Next Rank: 500 Posts
- Posts: 406
- Location: Syracuse, NY
- Thanked: 23 times
- GMAT Score:740
I categorize the intersections as one of two types:
(1) those created by diagonal lines
(2) those created by horizontal/vertical lines
You can see that each identical square has 1 intersection created by diagonal lines.
In this type of grid, which contains identical squares and has 'N' rows and 'N' columns, there are N^2 intersections from diagonal lines
Now look at the top row. Notice that there are 5 vertical lines which intersect the top-most horizontal line.
In this type of grid, which contains identical squares and has 'N' rows and 'N' columns, there are (N+1)^2 intersections created by horizontal/vertical lines.
In a 5x5 grid, N=5. There are N^2 = 25 intersection points from diagonal lines
There are also (N+1)^2 = 36 intersection points from horizontal/vertical lines.
There are no other types of intersections, so the total # of intersections = 25+36=61.
(1) those created by diagonal lines
(2) those created by horizontal/vertical lines
You can see that each identical square has 1 intersection created by diagonal lines.
In this type of grid, which contains identical squares and has 'N' rows and 'N' columns, there are N^2 intersections from diagonal lines
Now look at the top row. Notice that there are 5 vertical lines which intersect the top-most horizontal line.
In this type of grid, which contains identical squares and has 'N' rows and 'N' columns, there are (N+1)^2 intersections created by horizontal/vertical lines.
In a 5x5 grid, N=5. There are N^2 = 25 intersection points from diagonal lines
There are also (N+1)^2 = 36 intersection points from horizontal/vertical lines.
There are no other types of intersections, so the total # of intersections = 25+36=61.
I'm really old, but I'll never be too old to become more educated.
