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28 Apr 2022, 06:42
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D
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Difficulty:
45%
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68% (02:00) correct
32%
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wrong
based on 44
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In the figure above, the centers of circles W, X, Y, and Z are joined to form a quadrilateral. Circle W is identical to circle Y and circle X is identical to circle Z, and each of the circles is tangent to either two or three other circles, as shown. Is quadrilateral WXYZ a square?
(1) The circumference of circle W is equal to the circumference of circle X.
(2) The sum of the radii of circles W and Y is one-half the sum of the diameters of circles X and Z.
Attachment:
2022-04-28_17-41-18.png [ 19.72 KiB | Viewed 2255 times ]
28 Apr 2022, 22:24
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Bunuel
Statement 1 - Circumference of circle W is equal to the circumference of circle X.
Radius of Circle W is equal to radius of Circle X
Circle W is identical to Circle X. In fact, all the 4 circles are identical.
All the sides of the quadrilateral will be equal to the diameter of any one circle. However the diagonals are not equal. Diagonal WY is equal to the diameter of any circle but diagonal XZ will be greater than the diameter. The figure is not a square.
Sufficient to answer
Statement 2 The sum of the radii of circles W and Y is one-half the sum of the diameters of circles X and Z
The sum of radii of W and Y is equal to sum of the radii of X and Z. W and Y are identical, X and Z are identical. All the 4 circles are identical.
Sufficient
Option D
27 Feb 2023, 01:31
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How did you conclude "The sum of radii of W and Y is equal to sum of the radii of X and Z" when the statement says "Statement 2 The sum of the radii of circles W and Y is one-half the sum of the diameters of circles X and Z" ->
Rw+Ry = 1.5 (2Rx+2Rz)?
Rw+Ry = 1.5 (2Rx+2Rz)?
