If the average of 64, 69, 72, 75, x lies between 62 and 76 (excluding 62 and 76), then what is the number of possible integer values of x?

Explanation

The sum of the four given numbers is 280. The average is \frac{280+x}{5}. Thus, 62 \lt \frac{280+x}{5} \lt 76, which simplifies to 310 \lt 280+x \lt 380, so 30 \lt x \lt 100. The number of integers between 30 and 100 is 99 - 31 + 1 = 69.

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