How far is point P from point Q? (All points lie on a straight line.) I. Point T is exactly midway between P and Q. Point T is 5 km west of point R. II. Point Q is 2 km east of point R.

Introduction / Context:
We must compute the exact distance between two collinear points, P and Q, using reference points T and R. Sufficiency hinges on whether a unique numeric distance results.

Given Data / Assumptions:

• I: T is the midpoint of segment PQ and T is 5 km west of R.
• II: Q is 2 km east of R.
• Positive eastward direction; west is negative relative to R for a simple coordinate model.

Concept / Approach:
Place R at coordinate 0. Use directional data to place T and Q, then apply the midpoint relation to solve for P and hence the distance PQ.

Step-by-Step Solution:

Verification / Alternative check:
Reverse-check midpoint: (−12 + 2)/2 = −10/2 = −5, consistent with T's position.

Why Other Options Are Wrong:

• A/B/C: Neither statement alone fixes unique coordinates; hence not sufficient individually.
• D: Together they are sufficient.

Common Pitfalls:
Sign errors with east/west; forgetting midpoint formula requires absolute positions, not just relative gaps.

Final Answer:
Both statements together are sufficient, but NEITHER alone is sufficient.