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 →

MANHATTAN GMAT QUESTION COORDINATE GEOMETRY

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 24
Joined: Mon Jul 02, 2007 6:22 am
by karthick451 » Thu Sep 20, 2007 7:45 pm
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

A 4
B 6
C 8
D 10
E 12

ANY HELP IS APPRECIATED.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Senior | Next Rank: 100 Posts
Posts: 45
Joined: Wed Jun 20, 2007 12:40 pm
Location: Cleveland, OH

by niks_01.27 » Thu Sep 20, 2007 8:45 pm
If this is supposed to be a GMAT question and then I assume that the vertices talked about here are of the square, where one of the vertices must be on origin. Then only 4 squares can be drawn.

What is the answer? Is it A

Will explain if its correct.
regards
niks...
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 24
Joined: Mon Jul 02, 2007 6:22 am

by karthick451 » Fri Sep 21, 2007 6:03 am
A is not the answer niks and it is a GMAT question.

I will give the answer after a few more responses.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1018
Joined: Tue Dec 12, 2006 7:19 pmFollowed by: 6 members
Thanked: 86 times

by mayonnai5e » Fri Sep 21, 2007 6:46 am
My guess is E. You can rotate the square along the vertex at the origin and 360 degrees. The 4 obvious positions are where two sides align with the x and y axis. However, there should be two other positions in each quadrant where the vertex will just so happen to fall on the integer coordinates. What's the OA?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 321
Joined: Tue Aug 28, 2007 5:42 am
Thanked: 1 times

by kajcha » Fri Sep 21, 2007 6:47 am
I will go with 12.

One vertex can lie on origin and one on any of these points

(10,0), (-10,0), (0,10), (0,10), (6,8), (6,-8), (-6,8), (-6,-8), (8,6), (8,-6), (-8,6), (-8, -6)

From any of these points and origin you can calculate other 2 points.

e.g. Suppose 3rd coordinate is at (x,y) - diagonally opposite to origin

so, distance between (x,y) and (6,8) will be 10

and distance between (x,y) and origing will be 10root2

For this example other 2 points will be (2,14) and (-3,4)

I don't think you would really need to calculate for each of these points individually. If you are able to prove one point fits the formala, I think you can safely assume others will satisfy too.

I would definitely like to see some other answers.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 24
Joined: Mon Jul 02, 2007 6:22 am

by karthick451 » Fri Sep 21, 2007 6:53 am
E is the answer.

Kajcha, I think you explanation is spot on. Kudos.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 460
Joined: Sun Mar 25, 2007 7:42 am
Thanked: 27 times

by samirpandeyit62 » Fri Sep 21, 2007 7:25 am
I agree with Kajcha the ans should be E 12, I solved it like
Kajcha only.
Regards
Samir
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 45
Joined: Wed Jun 20, 2007 12:40 pm
Location: Cleveland, OH

by niks_01.27 » Fri Sep 21, 2007 7:27 pm
Agree with 12. Thanks, kajcha for a good explanation.
regards
niks...
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1