On a survey regarding a race conducted among the groups, The "X" group spoke the
truth, The "Y" group lied and The "Z" group told the truth and lied, alternatively. Carla,
Michael, and Tim belong to the different groups- X, Y, and Z, not necessarily in the
same order. One of them won the race. Following are the statements of Carla, Michael,
and Tim regarding the race.
Carla: Tim won the race. Tim always speaks the truth. Tim obstructed me at the last
moment.
Tim: I hadn't obstructed Carla at the last moment. Michael won the race.
Michael: Carla won the race. Tim is not a member of the "Y" group.
Michael is a member of which group?
Answers
Given : The "X" group spoke the truth, The "Y" group lied and The "Z" group told the truth and lied, alternatively
the statements of Carla, Michael,
and Tim regarding the race.
Carla: Tim won the race. Tim always speaks the truth. Tim obstructed me at the last moment.
Tim: I hadn't obstructed Carla at the last moment. Michael won the race.
Michael: Carla won the race. Tim is not a member of the "Y" group.
To Find : Michael is a member of which group
Solution:
Assume Michael is from group X - Spoke truth
Michael: Carla won the race. Tim is not a member of the "Y" group.
Both above statement True
Carla: Tim won the race. Tim always speaks the truth. Tim obstructed me at the last moment.
Tim won the race. Tim always speaks the truth must be false as per our assumption. so Carla belongs to group Y .
and Tim did not obstruct Carla at the last moment.
Tim: I hadn't obstructed Carla at the last moment. ( True)
Michael won the race. ( False) Hence Tim is Z
Assume Michael is from group Y
Michael: Carla won the race. Tim is not a member of the "Y" group.
=> Tim is a member of the "Y" group. which is not possible.
Hence NOT possible
Assume Michael is from group Z
Michael: Carla won the race. Tim is not a member of the "Y" group.
Case 1 : Carla won the race ( True ) and Tim is not a member of the "Y" group ( F)
=> Tim is a member of the "Y"
Tim: I hadn't obstructed Carla at the last moment. Michael won the race.
Tim obstructed Carla at the last moment.
Michael did not win the race.
Carla must be from Group X
Carla: Tim won the race. ( not possible )
Tim always speaks the truth. ( not possible )
Tim obstructed me at the last
Hence Not Possible
Case 2 :
Carla won the race ( False ) and Tim is not a member of the "Y" group ( T)
=> Carla did not won the race
Hence Tim Must be from Group X and Carla from Y
Tim: I hadn't obstructed Carla at the last moment. Michael won the race. all True
Carla: Tim won the race . Tim always speaks the truth. (T) Tim obstructed me at the last
Hence not possible.
SO FINALLY
Michael is from group X
Carla is from group Y
Tim is from group Z
Carla won the race
Tim is not a member of the "Y" group. ( Tim is from group Z)
Tim did not won the race.
Tim does not always speaks the truth.
Tim did not obstructed Carla at the last moment.
Michael did not won the race
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