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This problem trains for: SAT-I, AMC-8, GMAT.

After an encounter with some killer whales, a school of fish is reduced to eight ninths of its initial count. There were more than 1000 fish initially. What is the minimum number of fish the whales may have killed?

Since no half fish can be counted as being alive, then the number of fish must have been some multiple of nine. In other words, if the initial number of fish was N, the number of fish eaten is:

equation

and must be integer, therefore N is a multiple of 9, such as:

equation

The smallest possible number of fish that is greater than 1000 is 1008.

Therefore, the whales may have killed a minimum of:

equation