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  3. The greatest of the 21 positive integers in a certain list is 16. The median of

The greatest of the 21 positive integers in a certain list is 16. The median of

游客2025-02-24  32
问题 The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average(arithmetic mean)of the 21 integers?
选项 A、4
B、5
C、6
D、7
E、8
答案 C
解析 You are given that the median of the 21 positive integers is 10 and the greatest of the 21 integers is 16. This means that when the 21 integers are listed in order from least to greatest,
    the 1st through 10th integers are between 1 and 10, inclusive;
    the 11th integer is 10;
    the 12th through 20th integers are between 10 and 16, inclusive; and
    the 21st integer is 16.
The least possible average of the 21 integers would be achieved by using the least possible value of each integer as described above in the reordered list:
    the 1st through 10th integers would each be 1;
    the 11th integer would be 10;
    the 12th through 20th integers would each be 10; and
    the 21st integer would be 16.
For the least possible integers, the sum is(10)(1)+ 10 +(9)(10)+ 16, or 126. Therefore the least possible average is 126/21, or 6. The correct answer is Choice C.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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