The Virtual Environment for Reactor Applications (VERA) Core Physics Benchmark Progression Problems reported by the Consortium for Advanced Simulation of Light Water Reactors (CASL) were thoroughly analyzed using the UNIST inhouse Monte Carlo code MCS. Verification and validation of MCS toward Problem 5, startup Zero Power Physics Tests (ZPPT) results for Watts Bar Nuclear 1 (WBN1) Cycle 1, was conducted. The ZPPT series including critical eigenvalues, control bank worth, soluble boron worth, and the isothermal temperature coefficient obtained from MCS shows great accuracy with the KENO-VI and measured data. Furthermore, the capability of MCS for whole-core calculation with thermal-hydraulics feedback was proved by using the VERA Benchmark Problems 6 and 9 for WBN1 Cycle 1. Results for single-assembly at beginning-of-cycle and hot full power conditions demonstrated good agreement with VERA-CS solutions. The correlation between measured and simulated depletion results was reasonable, with the overall reactivity being predicted within 50 ppm of measurement.