LSAT-5-2-3

3. In Europe, schoolchildren devote time during each school day to calisthenics. North American schools rarely offer a daily calisthenics program. Tests prove that North American children are weaker, slower, and shorter-winded than European children. We must conclude that North American children can be made physically fit only if they participate in school calisthenics on a daily basis.

Which one of the following is assumed in the passage?

(A) All children can be made physically fit by daily calisthenics.

(B) All children can be made equally physically fit by daily calisthenics.

(C) Superior physical fitness produces superior health.

(D) School calisthenics are an indispensable factor in European children’s superior physical fitness.（D）

(E) North American children can learn to eat a more nutritious diet as well as to exercise daily.

I understand D is right, my question is why A is not an assumption since only if all children (regardliess they are North American kids or England kids) can be made physically fit by daily calisthnics, the North American can be made physically fit by participating in daily calisthnics. On the contrary, if "not all children can be made physically fit by daily calisthenics, even if "school calisthenics are an indispensable factor (not only factor) in European children (answer D), daily participation in calisthenics can't gurantee that North American kids will be made physiclaly fit.

II also noticed in the conclusion "

We must conclude that North American children can be made physically fit only if they participate in school calisthenics on a daily basis." "only if " means "daily calisthenics" is the "necessary condition" for being physically fit. However, I don't know what "being necessary condition" really mean when we choose the right answer. Doesn't it mean that we don't need to choose an answer that is the "sufficient condition" but only choose the answer acting as the 'necessary condition'?