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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

In a set of values, the range is 46, the smallest value is -5 and the mean is 13. If we eliminate the largest and the smallest values, the average of the remaining values is 8. How many values are there in the data set?

Denote the range with R, the largest value with L and the smallest value with s.

We can compute the largest value:

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Denote the number of values in the original data set with N. After eliminating the largest and the smallest values we obtain a subset with N-2 values. Computed from their average, the sum of all the values in this subset is:

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The average (arithmetic mean, mean) of the values in the whole set is:

equation

This is an equation we can solve for N.

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There were 4 values in the initial set.