The correct responses regarding why fifteenth-century Europeans searched for a sea route to Asia are:
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Europeans had begun to demand valuable goods, such as silk and spices, that could only be found in Asia.
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The Ottoman Turks controlled the Silk Road, which was the main land route from Europe through the Middle East to Asia.
While the interest in Asian culture and trade existed, the primary motivations were driven by the demand for goods and the geopolitical situation affecting trade routes.