Question

If X and Z each change color exactly once during a certain period and if, as a
result of these changes X is green and Z is orange, which of the following must
be true about that period?

• A. \( \text{X changed color before Z did.} \)
• B. \( \text{Z changed color before X did.} \)
• C. \( \text{X was purple before it changed color.} \)
• D. \( \text{Z was purple before it changed color.} \)
• E. \( \text{Z was red before it changed color.} \)

Hint:

Trace valid color transitions.

Answer 1

Answer: (E)

Step 1: X ends green, Z ends orange; each changes once, \( X \neq Z \).
Step 2: Valid changes: red to/from green, red to/from orange, red to/from purple, purple to/from orange.
Step 3: Z to orange requires red to orange (only direct path); X to green needs red to green.
Step 4: (E) Z was red is must, others depend on order or initial color.