Question

A driver must pick up exactly eight passengers—P, R, S, T, V, X, Y, and Z—one at a time, not necessarily in that order. The pickups must be made in accordance with the following conditions:

Either T or V must be picked up fifth.
Either Y or Z must be picked up third.
The driver picks up exactly one passenger between picking up T and picking up Z.
S is picked up eighth when Y is picked up third.
Z must be picked up ahead of T.

If V is picked up fifth, which one of the following must be true?

a) P is picked up first.

b) R is picked up sixth.

c) S is picked up eighth.

d) X is picked up seventh.

e) Z is picked up sixth.

Answer 1

Based on the given conditions and the requirement for V to be picked up fifth, it's not possible to deduce which of the given options must be true, because there is no direct relation mentioned in the problem between V's pickup order and the other passengers.

Step-by-step explanation:

The question presents a logic puzzle involving sequencing. It details the conditions under which a driver must pick up eight passengers with various constraints. If V is picked up fifth, we know the following from the given conditions: Z must be picked up ahead of T, suggesting Z is picked up first, second, third, or fourth. However, Y or Z is picked up third, so Z must be third. Since Z is picked up third and V fifth, T must be picked up fourth or sixth. Since there must be exactly one passenger between T and Z, and Z is third, T must be picked up fifth, but this contradicts the condition that V is fifth. Therefore, T must be picked up sixth. This leads us to conclude that option (e), Z is picked up sixth, is incorrect since it would not allow T to be picked up sixth. Moreover, there is no mention of the pickup order for P, R, S, or X in relation to V being picked up fifth in the information provided, implying none of the alternatives (a) through (d) are necessarily true given the conditions. Therefore, none of the given options must be true.