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by naveen451 » Sat Aug 13, 2011 1:32 am
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
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by pemdas » Sat Aug 13, 2011 1:53 am
four squares in each quadrant is clear so far.

next, we need to set the side of square equal to 10 and assume this side as hypotenuse of right triangle where the non-hypotenuse sides will be integers; 100=10^2 and 100=36+64. So we have 6 and 8 on x and y coordinates additionally, which makes additional two squares in each quadrant.

4+4*2=12

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naveen451 wrote: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
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by GMATGuruNY » Sat Aug 13, 2011 2:05 am
I posted a solution here:

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