Explanation

The average is (64 + 69 + 72 + 75 + x)/5 = (280 + x)/5. The condition 62 < (280+x)/5 < 76 gives 310 < 280 + x < 380, i.e. 30 < x < 100. The integers strictly between 30 and 100 are 31, 32, …, 99 — a total of 99 − 31 + 1 = 69 values, option (b).