Final answer:
Las Vegas is known as Sin City and is Nevada's largest city founded in the 1900s, experiencing growth due to gambling and major projects like the Hoover Dam.
Step-by-step explanation:
Nevada's largest city, nicknamed Sin City, and the most populous city founded in the 1900s is Las Vegas. Las Vegas experienced significant growth due to a combination of factors including the legalization of casino gambling in 1931 and the construction of the Hoover Dam.
While mining in the 19th century contributed to the boom and bust of towns such as Virginia City, it was also the precursor to more sustained growth as the West sought stability and governance to support its growing population and industry.