Segment Length in Ratio Problem

Very Hard Problem Solving Geometry

In triangle XYZ, point P lies on segment XY, such that the ratio of the length of segment XP to segment PY is 2:3. If the length of segment XY is 25 units, what is the length of segment XP?

Statement (1): The length of segment XZ is 15 units.

Statement (2): The length of segment YZ is 20 units.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

Hint

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