Step 1: Identify the key feature described in the question: the population was first split into two groups based on gender, and then members were picked from within each of those groups separately.
Step 2: Match this feature against each sampling method one by one instead of starting from stratified sampling. Ask: does the method involve dividing the population into meaningful subgroups before sampling, and sampling from each of them?
Step 3: Cluster sampling fails this test because whole clusters, not individuals within them, are the sampling units, and typically only some clusters are chosen, not all. Systematic sampling fails because it relies only on a fixed interval through an ordered list, with no subgrouping by any characteristic. Simple random sampling fails because there is no subgrouping step at all.
Step 4: Only one sampling design matches both features described, dividing into meaningful subgroups (strata) based on gender, and then drawing sample members from within each subgroup.
Step 5: That design is stratified sampling, since gender acts as the stratifying variable here.\[\boxed{\text{Stratified sampling}}\]