Given the set 2 3 5 7 11 12 x, the median is 7. Thus, if 1 is summed to x, the median does not change, thus x must be a number from 7 on. In addition, we know that when 1 is subtracted from x, then the median diminishes by 1. This must be that the median becomes 6 when 1 is subtracted from x. Now, which number from 7 on when is reduced by one make the median becoming 6? Only x = 7. Then, the set would become 2 3 4 5 7 7 11 12, thus the median is 7. When we include x+1 = 8 the median stays 7. When we include x-1=6, the median becomes 6. Here we are!