Question

The median of 11 different positive integers is $15$ and seven of those 11 integers are $8, 12, 20, 6, 14, 22,$ and $13$ .

Statement I: The difference between the averages of four largest integers and four smallest integers is $13.25$ .

Statement II: The average of all the 11 integers is $16$ .

Which of the following statements would be sufficient to find the largest possible integer of these numbers?

Accepted Answer

E. Known 7 numbers sorted: 6, 8, 12, 13, 14, 15 (median), 20, 22. Statement I gives the sum of 4 largest integers, allowing us to maximize the largest integer by setting others to minimal allowed distinct values. Thus Statement I is sufficient. Statement II gives the total sum of 11 integers, which also allows maximizing the largest integer. Thus Statement II is sufficient. Either Statement I or Statement II is sufficient.

Data Sufficiency on Median and Averages

Explanation

Practise this under exam conditions