Hoping my logic holds up:
1) If X is Red true then Y is not red also true: Contradicts initial premise that only one of given statements is true. Hence X is not Red. X is Blue or White.
2) If Y is not Red then it is Blue or White. If Z is not Blue then it is Red or White.
3) If Y not Red is true then Z not Blue is false as only one of these statements can be true. In which case Z is blue and 2) above means Y is white. However this would mean X is red which contradicts 1) above.
4) With Z not blue true, Y not Red is false. Y is red, 2) gives Z white and 1) gives X blue.
Lines up with statements given as follows:
X is Red - False. X is Blue.
Y is not Red - False. Y is Red
Z is not Blue - True. Z is White