Concept:
The Gutenberg Discontinuity is the boundary that separates the earth's mantle from the outer core. It is identified by a sudden change in seismic wave behaviour, where P-waves slow down and S-waves stop because the outer core is liquid.
Step 1:
The earth's interior is divided into crust, mantle and core. The boundary between crust and mantle is the Mohorovicic (Moho) discontinuity, while the boundary between the mantle and the core is the Gutenberg discontinuity.
Step 2:
The mantle extends to a depth of about 2900 km below the surface, and below this lies the core. Hence the Gutenberg discontinuity is located at roughly 2900 km depth.
Answer: Option (2) — 2900 km.