Direction: Read the following information carefully and answer the questions…

Concept:

In coded direction problems the two-digit number in brackets is read in reverse to get the actual distance, and the symbol fixes the cardinal direction (# = East, blank = North, % = West, @ = South). Place every point on an East-North grid, then the shortest distance between two points is the straight-line (Pythagorean) displacement, not the path walked:

distance = (ΔEast)2 + (ΔNorth)2 under a square root.

Application (trace only the X → S chain):

1. Take X as the origin (0, 0).

2. W @ (61) X → reverse 61 = 16, @ = South: W is 16 South of X, so W = (0, −16).

3. W % (45) U → reverse 45 = 54, % means W is West of U, so U is 54 East of W: U = (54, −16).

4. T (42) U → reverse 42 = 24, blank = North: T is 24 North of U, so T = (54, 8).

5. T # (03) S → reverse 03 = 30, # means T is East of S, so S is 30 West of T: S = (24, 8).

So S relative to X is 24 m East and 8 m North — i.e. towards the north-east.

Compute the shortest distance:

distance = √(242 + 82) = √640 ≈ 25.3 m.

Cross-check / contrast:

√640 ≈ 25.3 m is not exactly 25 m, and the only other displacement that is genuinely north-east here is this one. The listed values 16 m, 24 m, 8 m and 25 m do not equal √640 m (24 m and 8 m are merely the leg lengths, not the resultant; 25 m would need legs 24 and 7). Since the true north-east displacement √640 ≈ 25.3 m matches none of the printed values, the correct response is “None of these.” The R–Q–P chain and the S–R link do not lie on the X→S path, so they do not affect this answer.