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i dont have its official answer

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i dont have its official answer

by sana.noor » Wed Aug 21, 2013 9:59 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
Last edited by sana.noor on Thu Aug 22, 2013 12:21 am, edited 1 time in total.
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by ganeshrkamath » Wed Aug 21, 2013 11:12 pm
sana.noor wrote:How many circles can you form with origin as a center and radius of 10?
a. 4
b. 6
c. 8
d. 10
e. 12
Are you sure the question is right?
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by sana.noor » Thu Aug 22, 2013 12:22 am
Edited
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by ganeshrkamath » Thu Aug 22, 2013 12:36 am
sana.noor 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
One point is at the origin.
The distance between another vertex and the origin is 10.
(x-0)^2 + (y-0)^2 = 10^2
x^2 + y^2 = 100
(x,y) = (10,0) or (0,10) or (-10,0) or (0,-10) or (8,6) or (6,8) or (-8,6) or (-6,8) or (8,-6) or (6,-8) or (-6,-8) or (-8,-6)
Each of these can form a unique square. So total number of squares that can be formed = 12

Choose E

Draw a graph and it will become more clear.

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by GMATGuruNY » Thu Aug 22, 2013 2:55 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
Step 1: If area = 100, side = 10.
Step 2: Recognize that the hypotenuse of a 6-8-10 triangle is 10.
Step 3: Plot coordinate pairs using every possible combination of (±6,±8), (±8,±6),(0,±10) and (±10,0).
Step 4: Use the plotted points to draw as many squares as possible, making sure that each square has a vertex at the origin:

Image

The figure above shows that the number of possible squares = 12.

The correct answer is E.
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by kuzzden » Tue Sep 10, 2013 5:13 am
Hi, I can't get one point, can u please help:

from the quiestion: "One of the vertices must be on the origin..."

vertex - point at the intersection of two edges? am i wrong with this understanding? if not than posted solutions seem to be wrong...
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by sanjoy18 » Wed Sep 11, 2013 9:55 am
Just wanted to point out that wording of this problem is very important..Answer 12 is correct answer as it is mentioned that "all coordinates of the vertices must be integers".

If it was not mentioned in the question then answer would have been Infinity
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