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This problem trains for: AMC-8, Math Kangaroo 7-8, AMC-10.

In the unit cube MNJLCPAK: point B is the midpoint of the segment KJ, point F is the center of the face MNCP, point D is the midpoint of the segment ML. Which of the following inequalities is correct?

figure

figure

Compute the lengths of the segments in question using the Pythagorean theorem:

equation

equation

equation

equation

equation