Data Sufficiency on Median and Averages
XAT 2015 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability
The median of 11 different positive integers is and seven of those 11 integers are and .
Statement I: The difference between the averages of four largest integers and four smallest integers is .
Statement II: The average of all the 11 integers is .
Which of the following statements would be sufficient to find the largest possible integer of these numbers?
- A.
Statement I only.
- B.
Statement II only.
- C.
Both Statement I and Statement II are required.
- D.
Neither Statement I nor Statement II is sufficient.
- E.
Either Statement I or Statement II is sufficient.
E
Explanation
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.
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