How were old imperialism and new imperialism similar?
imperialists sought gold, cash crops, and trade goods.
asia was a major focus of colonization.
imperialists aimed to build large empires.
colonies existed for the benefit of a mother country.

The correct answer is: "Colonies existed for the benefit of a mother country".

Old imperialism was characterized by direct occupation and dominance of a territory, and mostly started with the arrival of the Spanish to America leaded by Columbus in 1492. Colonized territories depended on their mother country for political, economic, social and cultural issues.

New forms of imperialism, also called neocolonialism, do not necessarily involve occupation or "physical" dominance of a territory but, on the other hand, through the dynamics of capitalism and globalization, certain powerful  and developed countries are able to exercise power over other devoloping nations, which become dependent on the first.

In both cases, the relationships established are mostly profitable for the mother country, specially in economic terms. Old colonialism allowed the mother country to consume raw materials, minerals and other resources from the colonies and to use them to produce manufactures, aiming to become exporting nations. Nowadays, such system is not extinct at all as powerful countries buy cheap raw materials from developing countries, use them to manufacture products, and subsequently sell these final products in the international markets and even back in the developing country where they got the resources, earning large profits.

1st and 3rd : ) now lemme smash