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Let the parallelogram be like
.................x+2
.....A.______________B
.x.../|........................../|
..../..|......................../..|
D/__|___________/__|
.......E..................C...F
Nothing gets us the differences between the diagonals (we at least need to know the individial lengths and angles to calculate the diagonals as hypotenuse of right triangles).
Thus insufficient.
(2) Angle ABC = 30.
Therefore, CF = DE = x sqrt(3)/2 and
AE = BF = x/2
[CF = x cos 30 and BF = x sin 30]
Therefore, BD^2 = (x+2 +x sqrt(3)/2)^2 + (x^2)/4
Similarly, we can compute AC^2.
But both are in terms of x (and likely the second power of it).
Therefore, their difference can't be computed without knowing the value of x.
Therefore (E).
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