Explanation

For x > 0, x + 100/x > 50 is equivalent to x^2 - 50x + 100 > 0. The roots of x^2 - 50x + 100 = 0 are 25 +/- 5*sqrt(21), about 2.09 and 47.91. Since the parabola opens upward, the inequality holds for x < 2.09 or x > 47.91. Among natural numbers 1..100 this gives x = 1, 2 (2 values) and x = 48..100 (53 values), i.e. 2 + 53 = 55 values. Hence option (c).