The answer to this item could be identified by assigning x as the third number and equating the average of the scores as 80 or 90.
80:
80 = (78 + 95 + x)/3
The value of x from the equation is equal to 67.
90:
90 = (78 + 95 + x) / 3
The value of x from the equation is equal to 97.
Thus, the score should be 67 ≤ x ≤ 97.
The answer is the first choice.