Last visit was: 25 Jul 2024, 07:59 It is currently 25 Jul 2024, 07:59
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
CEO
CEO
Joined: 26 Feb 2016
Posts: 2863
Own Kudos [?]: 5337 [29]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Most Helpful Reply
Senior Manager
Senior Manager
Joined: 05 Jan 2017
Posts: 412
Own Kudos [?]: 286 [9]
Given Kudos: 15
Location: India
Send PM
General Discussion
CEO
CEO
Joined: 26 Feb 2016
Posts: 2863
Own Kudos [?]: 5337 [2]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 94614
Own Kudos [?]: 643792 [2]
Given Kudos: 86753
Send PM
Re: A Square is to be drawn on the xy-plane. If one vertex of the square [#permalink]
2
Bookmarks
Expert Reply
pushpitkc wrote:
A Square is to be drawn on the xy plane. If one vertex of the square needs to be at
the origin, sides of the square need to be 5 units each, and all coordinates of all
vertices need to be integers, how many different squares are possible?

A. 4
B. 6
C. 8
D. 12
E. 16

Source: Experts Global


Similar question to practice: https://gmatclub.com/forum/a-certain-sq ... 27018.html
Senior Manager
Senior Manager
Joined: 31 Jul 2017
Posts: 434
Own Kudos [?]: 450 [2]
Given Kudos: 752
Location: Malaysia
GPA: 3.95
WE:Consulting (Energy and Utilities)
Send PM
Re: A Square is to be drawn on the xy-plane. If one vertex of the square [#permalink]
2
Kudos
pushpitkc wrote:
A Square is to be drawn on the xy plane. If one vertex of the square needs to be at
the origin, sides of the square need to be 5 units each, and all coordinates of all
vertices need to be integers, how many different squares are possible?

A. 4
B. 6
C. 8
D. 12
E. 16

Source: Experts Global


Consider the First Quadrant -

The square can be formed with points when Y = 5,3,4 and X correspondingly will be X = 0,4,3. So, for each Quadrant there will be 3 Different Squares, hence for all the 4 Quadrants, it will be 12.
Intern
Intern
Joined: 11 Jun 2015
Posts: 15
Own Kudos [?]: 11 [1]
Given Kudos: 186
Location: Iran (Islamic Republic of)
Concentration: Accounting, Finance
WE:Education (Education)
Send PM
Re: A Square is to be drawn on the xy-plane. If one vertex of the square [#permalink]
1
Bookmarks
The square could rotate around the origin, making a cycle.
(x^2)+(y^2)=Diagonal of the square
(x^2)+(y^2)=50
Solving above Equation with Integer solutions=12
VP
VP
Joined: 29 Oct 2015
Posts: 1124
Own Kudos [?]: 474 [0]
Given Kudos: 679
GMAT 1: 570 Q42 V28
Send PM
A Square is to be drawn on the xy-plane. If one vertex of the square [#permalink]
KarishmaB chetan2u  KrishnakumarKA1
Will you be kind enough to show me how ,  starting with the point (-3,4), we can form 4 different squares ?  Finding it a bit confusing to visualize..Any simpler approach..
KrishnakumarKA1 wrote:
Hi,

This is a very interesting question.

Easily someone could fall for the trap answer as 4 here.

If one visualize the squares only on the x and y axis, then they end up falling for the trap.

So the vertices need not be only on the x and y axis, they have mentioned all the vertices should be integers,

So, Let’s try to visualize it,

We can see that,

Co-ordinates (-4,3) forms a side length of the square as 5 from the origin (0,0), Because 3-4-5 are pythogorean triplets.

As shown in the figure(In the attachment), we can form four squares starting with point (-4,3).

So similarly starting with the point (-3,4), we can form 4 different squares.

Already on the x and y axis there are 4 different squares.

So totally, we can form 12 different squares with side length as 5 and one vertex at the origin. So the answer is D.

Most important factor of solving a co-ordinate geometry question is visualizing.

Hope this helps.

­
GMAT Club Bot
A Square is to be drawn on the xy-plane. If one vertex of the square [#permalink]
Moderator:
Math Expert
94614 posts