Data set $X$ consists of 10 positive integers less than 54. The list shown gives 9 of the integers from data set $X$.
$$23, 41, 29, 35, 46, 51, 15, 30, 45$$
The mean of these 9 integers is 35. If the mean of data set $X$ is an integer that is greater than 35, what is the value of the largest integer from the data set $X$?
20/22
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