Directions: Read the following details carefully and answer the questions that follow.

An office building has four levels, numbered 1 to 4 from bottom to top. Each level contains two office wings: the West Wing and the East Wing. The West Wing of level 2 is directly above the West Wing of level 1 and directly below the West Wing of level 3, and so on. Similarly, the East Wing of level 2 is directly above the East Wing of level 1 and directly below the East Wing of level 3, and so on. Eight professionals—P, Q, R, S, T, U, V, and W—each occupy one of these eight office wings. Each office wing houses exactly one professional.

There is a gap of one level between P and U. W works to the west of Q, who works to the northeast of U. P works to the southwest of S. R works to the east of T.

Which of the following statements is true?

Correct Answer: The true statement is Q and V work in the same wing.

Step-by-Step Explanation:

Step 1: Understand the Grid Structure
The office building consists of 4 levels (numbered 1 to 4 from bottom to top) with 2 wings per level (West Wing and East Wing). This creates a grid of 8 positions:
• West Wing: 4 positions (Levels 1, 2, 3, 4)
• East Wing: 4 positions (Levels 1, 2, 3, 4)

Step 2: Classify Each Professional by Wing
We can determine which wing each of the 8 professionals (P, Q, R, S, T, U, V, W) belongs to using the directional clues given in the problem statement:
1. "W works to the west of Q" ⇒ W is in the West Wing, and Q is in the East Wing (on the same level).
2. "Q works to the northeast of U" ⇒ Since Q is in the East Wing, for Q to be to the northeast of U, U must be in the West Wing.
3. "P works to the southwest of S" ⇒ For P to be southwest of S, P must be in the West Wing, and S must be in the East Wing.
4. "R works to the east of T" ⇒ T is in the West Wing, and R is in the East Wing (on the same level).

Grouping the professionals by wing:
• West Wing Professionals: W, U, P, T
• East Wing Professionals: Q, S, R, V (since V is the 8th remaining professional)

Notice that both Q and V work in the East Wing. This immediately validates the statement that Q and V work in the same wing.

Step 3: Determine the Complete Level-by-Level Layout
To verify all the other statements, let's solve for the exact floor placement of each person:
• There is a gap of one level between P and U in the West Wing. Their levels must be 1 and 3, or 2 and 4.
• Q is to the northeast of U, meaning Level of Q > Level of U. Since Q and W share the same level, Level of W > Level of U.
• P is southwest of S, meaning Level of S > Level of P.
• Testing U on Level 3 and P on Level 1:
- Level 4: West Wing = W, East Wing = Q (Since Level of Q > Level of U)
- Level 3: West Wing = U, East Wing = S (Since S is on a level above P)
- Level 2: West Wing = T, East Wing = R (Since R is east of T)
- Level 1: West Wing = P, East Wing = V (Remaining position for V)

Step 4: Evaluate the Given Options
• S works on the level below U in the same wing: False (S and U are on the same level, Level 3, in different wings).
• T and W work on consecutive levels: False (T is on Level 2 and W is on Level 4).
• P works on the level above R: False (P is on Level 1 and R is on Level 2, so P is below R).
• Q and V work in the same wing: True (Both Q and V work in the East Wing).
• V works northwest of T: False (V is on Level 1 East and T is on Level 2 West, making V southeast of T).

Thus, the correct statement is that Q and V work in the same wing.