Sufficiency implies Sufficiency and Necessity

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Is it correct to say that: if for a problem exist a sufficient condition, then will mandatorily exist a sufficient and necessary condition (even if we have not discovered it yet) ?

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No, that is not always true.

For example if $x<5$, then $x<6$ but if $x<6$ we can not conclude that $x<5$ That is $x<5$ is sufficient for $x<6$ but it is not necessary for $x<6$