Is it possible that some condition is not necessary but yet sufficient?
As far as I know a sufficiency entails necessity. If something is not necessary then it can not be sufficient. Is that right?
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Yes, a condition can be sufficient but not necessary. For example, being in Paris is sufficient for being in France, but it is not necessary. More: running 20km every day is sufficient for being in good shape, but not necessary. Being 80 is sufficient for being old, but not necessary.
More generally, in any case where X is a strict subset of Y, being a member of X is sufficient, but not necessary, for being a member of Y.