More efficient and most efficient are the comparative and superlative forms of "efficient".

Yes, organizations can be efficient, but ineffective. Efficient means that they have little waste. Effective means that they are good at what they do.

computer maintenance is essential for effective and efficient management in an organization computer maintenance is essential for effective and efficient management in an organization computer maintenance is essential for effective and efficient management in an organization

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To be efficient means to be quick and effective at a job or task.