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

The average of one hundred values has been calculated to be 27. If the smallest recorded number was 12, what would be the ratio between the largest possible number and the smallest one?

The largest possible value occurs if all other values are the lowest possible.

Denote the largest value with L and the smallest value with l. Using the definition of the average:

Substitute the value of l: