squares, co-ordinates

[vmahi7]

Jessie made a square of side with 5 cm whose one vertex is at origin.The co-ordinates of the square made by Jessie are integers,how many such squares are possible..?

[Brent@GMATPrepNow]

Jessie made a square of side with 5 cm whose one vertex is at origin.The co-ordinates of the square made by Jessie are integers,how many such squares are possible..?

This question is a knockoff of this one: https://www.beatthegmat.com/how-many-dif ... 78228.html

The only difference is that the right triangles with sides 6-8-10 are replaced with right triangles with sides 3-4-5

The answer is still 12

Cheers,
Brent

[GMATinsight]

Jessie made a square of side with 5 cm whose one vertex is at origin.The co-ordinates of the square made by Jessie are integers,how many such squares are possible..?

For getting the answers of these question you should be Finding the points in only First Quadrant and on X-Axis as the number of points in each quadrant will be similar as other Quadrant are just the mirror images of adjacent quadrant about one of the axes.

With this, we realize that the answer must be a multiple of 4 therefore we Eliminate all options that are not multiple of 4

So here we look for the Integer values such that
X^2+Y^2 = 25 [Equation of Circle with radius 5 and centre at origin]

Now the famous triplet 3-4-5 comes into picture
One case when vertex is at (5,0) second when Vertex is at (3,4) and third is when the same vertex is at (4,3)

3 points multiplied by 4 as there will be 3 such points in each of the 4 Quadrants
Total points = 3x4 = 12

Answer: 12