Problem:
A list of integers has mode and mean . The smallest number in the list is . The median of the list is a member of the list. If the list member were replaced by , the mean and median of the new list would be and , respectively. If were instead replaced by , the median of the new list would be . What is
Answer Choices:
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Solution:
When is added to a number in the list, the mean increases by , so there must be five numbers in the original list whose sum is . Since is the smallest number in the list and is the median, we may assume
denoting the other members of the list by , and . Since the mode is , we must have ; otherwise, would be larger than . So . Since decreasing by decreases the median by must be less than . Solving and for gives .