# Which one of the following could be true?

Ryan on September 15, 2019

Irina on September 19, 2019

The game requires us to assign 4 architects - F G H L to 4 projects W X Y Z completed at different times, meaning it has a linear and a matching element to it.

The following rules apply:

(1) Either F or L is assigned to Z.

Z: F/L

(2) F is assigned W if G is not.

~ G (W) -> F (W)

We can infer that if F is not assigned W, then G must be assigned W. Thus, W must be assigned either F or G.

W: F/G

(3) H is assigned Y if F is not assigned W.

~F (W ) -> H (Y)

We can infer that if H is not assigned Y, F must be assigned W.

~H (Y) -> F (W)

And we can also combine it with a previous rule to conclude that if F is not assigned W, H is assigned Y, and G is assigned W.

~ F(W) -> H (Y) & G(W)

(4) F is completed immediately before G.

This rule tells us we must have an FG sequence.

(5) H project is completed last.

This rule tells us FG must either be 1 and 2 or 2 and 3.

The question asks which of the following could be true?

The question only concerns the order, so the rules regarding the assignments are irrelevant to it.

(A) G is first and L is second.

Incorrect. Rule tells us that we must have an FG sequence, so G cannot possible be first because F must come before it.

(B) F is completed 3D and H is completed 4th.

Incorrect. G must follow F per the rules, hence it is impossible for H to follow G.

(C) Lee's project is completed first, and G is second.

Incorrect. G must immediately follow F- FG per the rules, so LG sequence is impossible.

(D) F is completed second and L is completed 3D.

Incorrect. F must be followed directly by G per the rules, not L.

(E) Lee's project is completed first and F's second.

Correct. This will allow for the following order LFGH, which complies with all the rules.

Let me know if this makes sense and if you have any further questions.