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?

Sum of given four numbers = 64 + 69 + 72 + 75 = 280. Average = (280 + x)/5. We need 62 < (280 + x)/5 < 76, so 310 < 280 + x < 380, giving 30 < x < 100. The integer values are 31, 32, ..., 99, which gives 99 − 31 + 1 = 69 integers.