Directions: Select the correct alternative from the given choices. A data set comprises five natural numbers, 15, 4, 42, 23 and x. How many values of x exist such that the median of the above set of numbers is equal to its mean?

Sorted set: 4, 15, 23, 42, x. Mean = (4+15+23+42+x)/5 = (84+x)/5. If x is between 15 and 23, median is x. So x = (84+x)/5 => 5x = 84+x => 4x = 84 => x = 21 (valid). If x > 42, median is 23. So 23 = (84+x)/5 => 115 = 84+x => x = 31 (not > 42, invalid). If x < 4, median is 15. So 15 = (84+x)/5 => 75 = 84+x => x = -9 (not < 4, invalid). Checking other positions reveals 2 solutions.