@Zerks: Median is not the middle number, by number, in the set. Median is, after arranging the numbers of the set in descending order, the middle number, by value. I hope you understand this.
When you say 45 is the highest number, the lowest number must be 15 (range is 30). Agreed? All this means is after arranging 13 different integers in an order, and assuming highest and lowest ones to be 45 and 15 respectively, with 30 as median, there must be 6 integers whose values are lower than 30 but higher than 15. This condition can certainly be true with the highest value as 45.
Let's do the same with 54. Lowest number now must be 24. Median still remains 30. Again 6 mumbers must be below 30 and above 23. So the numbers can be 24, 25, 26, 27, 28, 29 (6 total). 30 would be a center or 7th number and then you can put any value to the remaining 6 that are above 30 but below 54.
As we saw, even 54 yields a correct answer. You pick the HIGHEST POSSIBLE VALUE, therefore 54 and not 45.
I hope you understood my exaplanation.
When you say 45 is the highest number, the lowest number must be 15 (range is 30). Agreed? All this means is after arranging 13 different integers in an order, and assuming highest and lowest ones to be 45 and 15 respectively, with 30 as median, there must be 6 integers whose values are lower than 30 but higher than 15. This condition can certainly be true with the highest value as 45.
Let's do the same with 54. Lowest number now must be 24. Median still remains 30. Again 6 mumbers must be below 30 and above 23. So the numbers can be 24, 25, 26, 27, 28, 29 (6 total). 30 would be a center or 7th number and then you can put any value to the remaining 6 that are above 30 but below 54.
As we saw, even 54 yields a correct answer. You pick the HIGHEST POSSIBLE VALUE, therefore 54 and not 45.
I hope you understood my exaplanation.
