Explanation


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 \(\frac{126}{21}\) or 6.

The correct answer is Choice C.
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There are 21 numbers in the list, and, if we list the numbers in ascending order, the median is the 11th number.

Thus, we can let each of the first 10 numbers = 1, each of the next 10 numbers = 10, and the last number = 16.

Thus, the average is (10 x 1 + 10 x 10 + 16)/21 = 126/21 = 6.

Answer: C
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