2025 AMC 8

Complete problem set with solutions and individual problem pages

Problem 14 Medium

A number N is inserted into the list 2, 6, 7, 7, 28. The mean is now twice as great as the median. What is N?

  • A.

    7

  • B.

    14

  • C.

    20

  • D.

    28

  • E.

    34

Answer:E

Solution 1

The median of the list is 7, so the mean of the new list will be 7 \cdot 2 = 14. Since there are 6 numbers in the new list, the sum of the 6 numbers will be 14 \cdot 6 = 84. Therefore, 2+6+7+7+28+N = 84 \implies N = \boxed{\text{(E) 34}}

 

Solution 2

Since the average right now is 10, and the median is 7, we see that N must be larger than 10, which means that the median of the 6 resulting numbers should be 7, making the mean of these 14. We can do 2 + 6 + 7 + 7 + 28 + N = 14 * 6 = 84. 50 + N = 84, so N = \boxed{\text{(E) 34}}

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